{"id":45295,"date":"2026-04-01T14:19:24","date_gmt":"2026-04-01T06:19:24","guid":{"rendered":"https:\/\/www.qiusir.com\/?p=45295"},"modified":"2026-04-02T16:11:05","modified_gmt":"2026-04-02T08:11:05","slug":"qiutopia%e7%90%86%e6%83%b3%e6%b0%94%e4%bd%93%e5%b0%8f%e5%b0%8f%e6%b5%8b%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=45295","title":{"rendered":"qiutopIA\u7406\u60f3\u6c14\u4f53\u7ebf\u4e0a\u5c0f\u6d4b\u9a8c"},"content":{"rendered":"\u4e00\u3001\u57fa\u7840\r\n\r\n<div id=\"qiusir-quiz-fixed-v12\" style=\"padding: 10px; font-family: -apple-system, system-ui, sans-serif; max-width: 600px; margin: 0 auto; color: #334155; background: #ffffff;\">\r\n    \r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q1<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u4e00\u5b9a\u8d28\u91cf\u7684\u7406\u60f3\u6c14\u4f53\uff0c\u5728\u4fdd\u6301\u4f53\u79ef\u4e0d\u53d8\u7684\u8fc7\u7a0b\u4e2d\uff0c\u82e5\u5176\u70ed\u529b\u5b66\u6e29\u5ea6\u5347\u9ad8\u4e3a\u539f\u6765\u7684 2 \u500d\uff0c\u5219\u6c14\u4f53\u7684\u538b\u5f3a\u53d8\u4e3a\u539f\u6765\u7684\u591a\u5c11\u500d\uff1f<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u9519\u8bef\u3002\u6839\u636e\u67e5\u7406\u5b9a\u5f8b\uff0c\u7b49\u5bb9\u53d8\u5316\u4e2d\u538b\u5f3a\u4e0e\u70ed\u529b\u5b66\u6e29\u5ea6\u6210\u6b63\u6bd4\uff0c\u6e29\u5ea6\u5347\u9ad8\u538b\u5f3a\u5e94\u589e\u5927\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. 0.5 \u500d<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, true, '\u6b63\u786e\uff01\u6839\u636e\u67e5\u7406\u5b9a\u5f8b P\/T = C\uff0c\u4f53\u79ef\u4e0d\u53d8\u65f6\u538b\u5f3a\u4e0e\u70ed\u529b\u5b66\u6e29\u5ea6\u6210\u6b63\u6bd4\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. 2 \u500d<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u9519\u8bef\u3002\u538b\u5f3a\u4e0e\u70ed\u529b\u5b66\u6e29\u5ea6\u662f\u4e00\u6b21\u65b9\u6b63\u6bd4\u5173\u7cfb\uff0c\u800c\u975e\u5e73\u65b9\u5173\u7cfb\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. 4 \u500d<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q2<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u5c06\u4e00\u5145\u6ee1\u7a7a\u6c14\u7684\u5bc6\u95ed\u5bb9\u5668\u4ece\u5ba4\u6e29 (27\u00b0C) \u52a0\u70ed\u5230 127\u00b0C\uff0c\u82e5\u5ffd\u7565\u5bb9\u5668\u70ed\u81a8\u80c0\uff0c\u6b64\u65f6\u6c14\u4f53\u7684\u538b\u5f3a\u53d8\u4e3a\u539f\u6765\u7684\u591a\u5c11\u500d\uff1f<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u6ce8\u610f\uff1a\u6bd4\u4f8b\u8ba1\u7b97\u5fc5\u987b\u4f7f\u7528\u70ed\u529b\u5b66\u6e29\u5ea6 K (T = t + 273)\uff0c\u4e0d\u80fd\u76f4\u63a5\u7528\u6444\u6c0f\u5ea6\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. 127\/27 \u500d<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, true, '\u6b63\u786e\uff01T1 = 300K, T2 = 400K\u3002\u6839\u636e P1\/T1 = P2\/T2\uff0cP2\/P1 = 400\/300 = 4\/3\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. 4\/3 \u500d<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u8ba1\u7b97\u6709\u8bef\u3002\u8bf7\u68c0\u67e5\u70ed\u529b\u5b66\u6e29\u5ea6\u7684\u6362\u7b97\u662f\u5426\u51c6\u786e\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. 1.5 \u500d<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q3<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u5173\u4e8e\u4e00\u5b9a\u8d28\u91cf\u7684\u7406\u60f3\u6c14\u4f53\uff0c\u4e0b\u5217\u8bf4\u6cd5\u4e2d\u6b63\u786e\u7684\u662f\u54ea\u4e00\u9879\uff1f<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u7406\u60f3\u6a21\u578b\u5047\u8bbe\u5206\u5b50\u95f4\u9664\u78b0\u649e\u77ac\u95f4\u5916\u6ca1\u6709\u76f8\u4e92\u4f5c\u7528\u529b\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. \u7406\u60f3\u6c14\u4f53\u5206\u5b50\u95f4\u5b58\u5728\u5f88\u5f3a\u7684\u5f15\u529b<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, true, '\u6b63\u786e\uff01\u7406\u60f3\u6c14\u4f53\u5ffd\u7565\u4e86\u5206\u5b50\u52bf\u80fd\uff0c\u5176\u5185\u80fd\u5b8c\u5168\u7531\u5206\u5b50\u7684\u70ed\u8fd0\u52a8\u52a8\u80fd\uff08\u6e29\u5ea6\uff09\u51b3\u5b9a\u3002\u6709\u60c5\u8da3\u53ef\u662f\u63a8\u5230U=3\/2pV')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. \u7406\u60f3\u6c14\u4f53\u7684\u5185\u80fd\u53ea\u4e0e\u6e29\u5ea6\u6709\u5173<\/button>\r\n            <button onclick=\"handleGasAnsV12(this, false, '\u6c14\u4f53\u7684\u4f53\u79ef\u662f\u6307\u6c14\u4f53\u6240\u80fd\u5145\u6ee1\u7684\u7a7a\u95f4\uff08\u5bb9\u5668\u5bb9\u79ef\uff09\uff0c\u800c\u975e\u5206\u5b50\u672c\u8eab\u7684\u4f53\u79ef\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. \u7406\u60f3\u6c14\u4f53\u7684\u4f53\u79ef\u662f\u6240\u6709\u5206\u5b50\u4f53\u79ef\u4e4b\u548c<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n    function handleGasAnsV12(btn, isRight, info) {\r\n        const wrap = btn.parentElement;\r\n        const feedback = wrap.nextElementSibling;\r\n        const btns = wrap.querySelectorAll('button');\r\n        \r\n        btns.forEach(b => {\r\n            b.disabled = true;\r\n            b.style.cursor = 'default';\r\n            b.style.opacity = '0.5';\r\n        });\r\n\r\n        feedback.style.display = 'block';\r\n        feedback.textContent = info;\r\n\r\n        if (isRight) {\r\n            btn.style.background = '#f0fdf4 !important';\r\n            btn.style.borderColor = '#22c55e !important';\r\n            btn.style.color = '#166534 !important';\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#f0fdf4';\r\n            feedback.style.color = '#166534';\r\n            feedback.style.border = '1px solid #bbf7d0';\r\n        } else {\r\n            btn.style.background = '#fef2f2 !important';\r\n            btn.style.borderColor = '#ef4444 !important';\r\n            btn.style.color = '#991b1b !important';\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#fef2f2';\r\n            feedback.style.color = '#991b1b';\r\n            feedback.style.border = '1px solid #fecaca';\r\n        }\r\n    }\r\n    <\/script>\r\n<\/div>\r\n\r\n\u4e8c\u3001\u8fdb\u9636\r\n<div id=\"qiusir-quiz-hard-v14\" style=\"padding: 10px; font-family: -apple-system, system-ui, sans-serif; max-width: 600px; margin: 0 auto; color: #334155; background: #ffffff;\">\r\n    \r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q1<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u4e00\u4e2a\u5bb9\u79ef\u4e3a $V$ \u7684\u771f\u7a7a\u94a2\u74f6\u4e0e\u538b\u5f3a $P_0$\u3001\u6e29\u5ea6 $T_0$ \u7684\u5927\u6c14\u76f8\u901a\u3002\u5145\u6c14\u7ed3\u675f\u540e\u74f6\u5185\u6e29\u5ea6\u5347\u81f3 $T_1$\uff0c\u5219\u74f6\u5185\u6c14\u4f53\u7684\u538b\u5f3a\u4e3a\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u5145\u6c14\u540e\u74f6\u5185\u6c14\u4f53\u7684\u7269\u8d28\u7684\u91cf\u5df2\u589e\u52a0\uff0c\u4e0d\u80fd\u7b80\u5355\u8ba4\u4e3a\u538b\u5f3a\u4ecd\u7b49\u4e8e\u5916\u754c\u5927\u6c14\u538b\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. $P_0$<\/button>\r\n            <button onclick=\"handleHardAns(this, true, '\u6b63\u786e\uff01\u5145\u6c14\u77ac\u95f4\u74f6\u5185\u6c14\u4f53\u5bc6\u5ea6\u4e0e\u5927\u6c14\u76f8\u540c\u3002\u7531 $PV=nRT$ \u77e5\uff0c\u5bc6\u5ea6\u76f8\u540c\u65f6\u538b\u5f3a\u4e0e\u70ed\u529b\u5b66\u6e29\u5ea6\u6210\u6b63\u6bd4\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. $\\frac{T_1}{T_0} P_0$<\/button>\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u6839\u636e\u67e5\u7406\u5b9a\u5f8b\uff0c\u6e29\u5ea6\u5347\u9ad8\u538b\u5f3a\u5e94\u589e\u5927\uff0c\u800c\u8be5\u9009\u9879\u6bd4\u503c\u5c0f\u4e8e 1\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. $\\frac{T_0}{T_1} P_0$<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q2<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u4e24\u8fde\u901a\u7b49\u5bb9\u5bb9\u5668 A\u3001B \u5145\u6ee1 $P_1, T_1$ \u6c14\u4f53\u3002\u4fdd\u6301 A \u6e29\u5ea6\u4e0d\u53d8\uff0c\u5c06 B \u52a0\u70ed\u5230 $T_2$\uff0c\u7a33\u5b9a\u540e\u7cfb\u7edf\u538b\u5f3a $P$ \u4e3a\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleHardAns(this, true, '\u6b63\u786e\uff01\u7531\u603b\u7269\u8d28\u7684\u91cf\u5b88\u6052$\\frac{P_1 \\cdot 2V}{RT_1} = \\frac{PV}{RT_1} + \\frac{PV}{RT_2}$\uff0c\u6574\u7406\u5373\u53ef\u5f97\u89e3\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. $\\frac{2T_2}{T_1 + T_2} P_1$<\/button>\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u8fd9\u662f\u6e29\u5ea6\u7684\u7b97\u672f\u5e73\u5747\u6bd4\u4f8b\uff0c\u5ffd\u7565\u4e86\u6c14\u4f53\u5728\u4e24\u5bb9\u5668\u95f4\u91cd\u65b0\u5206\u914d\u7684\u7269\u7406\u672c\u8d28\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. $\\frac{T_1 + T_2}{2T_1} P_1$<\/button>\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u6b64\u9879\u5047\u8bbe A \u4e2d\u6c14\u4f53\u5168\u90e8\u8dd1\u5230\u4e86 B \u4e2d\uff0c\u8fdd\u53cd\u4e86\u8fde\u901a\u5668\u7684\u538b\u5f3a\u5e73\u8861\u539f\u7406\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. $\\frac{T_2}{T_1} P_1$<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f8fafc; border-radius: 12px; border: 1px solid #e2e8f0;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q3<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u5bb9\u79ef $V$ \u7684\u5bb9\u5668\u539f\u538b\u5f3a $P_0$\uff0c\u62bd\u6c14\u673a\u6bcf\u6b21\u62bd\u6c14\u5bb9\u79ef $v$\u3002\u7b49\u6e29\u4e0b\u62bd\u6c14 $n$ \u6b21\u540e\uff0c\u538b\u5f3a\u53d8\u4e3a\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleHardAns(this, true, '\u6b63\u786e\uff01\u7b2c 1 \u6b21\u62bd\u6c14\u6ee1\u8db3 $P_0 V = P_1 (V + v)$\uff0c\u5373 $P_1 = P_0 [V\/(V+v)]$\u3002\u4ee5\u6b64\u7c7b\u63a8 $n$ \u6b21\u5373\u53ef\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. $P_0 (\\frac{V}{V + v})^n$<\/button>\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u8fd9\u662f\u5c06 $n$ \u6b21\u62bd\u6c14\u8bef\u8ba4\u4e3a\u662f\u4e00\u6b21\u6027\u81a8\u80c0\u5230 $V+nv$ \u7684\u4f53\u79ef\uff0c\u5ffd\u7565\u4e86\u5206\u6b21\u6392\u9664\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. $P_0 \\frac{V}{V + nv}$<\/button>\r\n            <button onclick=\"handleHardAns(this, false, '\u9519\u8bef\u3002\u8be5\u6bd4\u4f8b\u4e0d\u7b26\u5408\u7b49\u6e29\u81a8\u80c0\u540e\u8d28\u91cf\u6392\u9664\u7684\u7269\u7406\u903b\u8f91\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. $P_0 (1 &#8211; \\frac{v}{V})^n$<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n    \/\/ \u903b\u8f91\u8fd0\u7b97\u7b26 && \u548c || \u5df2\u88ab\u5d4c\u5957 if \u6216\u72ec\u7acb\u903b\u8f91\u66ff\u4ee3\r\n    function handleHardAns(btn, isRight, info) {\r\n        const wrap = btn.parentElement;\r\n        const feedback = wrap.nextElementSibling;\r\n        const btns = wrap.querySelectorAll('button');\r\n        \r\n        btns.forEach(b => {\r\n            b.disabled = true;\r\n            b.style.cursor = 'default';\r\n            b.style.opacity = '0.5';\r\n        });\r\n\r\n        feedback.style.display = 'block';\r\n        feedback.textContent = info;\r\n\r\n        if (isRight) {\r\n            btn.style.background = '#f0fdf4 !important';\r\n            btn.style.borderColor = '#22c55e !important';\r\n            btn.style.color = '#166534 !important';\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#f0fdf4';\r\n            feedback.style.color = '#166534';\r\n            feedback.style.border = '1px solid #bbf7d0';\r\n        } else {\r\n            btn.style.background = '#fef2f2 !important';\r\n            btn.style.borderColor = '#ef4444 !important';\r\n            btn.style.color = '#991b1b !important';\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#fef2f2';\r\n            feedback.style.color = '#991b1b';\r\n            feedback.style.border = '1px solid #fecaca';\r\n        }\r\n    }\r\n    <\/script>\r\n<\/div>\r\n\u4e09\u3001\u6311\u6218\r\n<div id=\"qiusir-quiz-challenge-v16\" style=\"padding: 10px; font-family: -apple-system, system-ui, sans-serif; max-width: 600px; margin: 0 auto; background: #ffffff;\">\r\n    \r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f0f9ff; border-radius: 12px; border: 1px solid #e0f2fe;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q1<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u6c34\u5e73\u6c14\u7f38\u6d3b\u585e\u5de6\u4fa7\u5c01\u95ed\u957f\u4e3a $L$\u3001\u538b\u5f3a\u4e3a $P_0$ \u7684\u6c14\u4f53\uff0c\u53f3\u4fa7\u901a\u5927\u6c14\uff08$P_0$\uff09\u3002\u7b49\u6e29\u4e0b\u5411\u5de6\u7f13\u6162\u63a8\u6d3b\u585e $L\/2$ \u8ddd\u79bb\uff0c\u6b64\u65f6\u65bd\u52a0\u5728\u6d3b\u585e\u4e0a\u7684\u63a8\u529b\u4e3a\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleExtremeAns(this, true, '\u6b63\u786e\uff01\u7531\u73bb\u610f\u8033\u5b9a\u5f8b\uff0c$P_1 L = P_2 (L\/2)$\uff0c\u5f97\u5185\u538b $P_2 = 2P_0$\u3002\u63a8\u529b $F = (2P_0 - P_0)S = P_0 S$\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. $P_0 S$<\/button>\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u8fd9\u662f\u6c14\u7f38\u5185\u90e8\u6c14\u4f53\u7684\u6700\u7ec8\u538b\u529b\uff0c\u8ba1\u7b97\u63a8\u529b\u65f6\u5fc5\u987b\u51cf\u53bb\u6d3b\u585e\u53f3\u4fa7\u53d7\u5230\u7684\u5927\u6c14\u538b\u529b\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. $2P_0 S$<\/button>\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u8be5\u6570\u503c\u4e0d\u8db3\u4ee5\u514b\u670d\u7531\u4e8e\u4f53\u79ef\u538b\u7f29\u5e26\u6765\u7684\u5185\u90e8\u538b\u5f3a\u589e\u91cf\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. $0.5P_0 S$<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f0f9ff; border-radius: 12px; border: 1px solid #e0f2fe;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q2<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u4e24\u4e2a\u7edd\u70ed\u5bb9\u5668 A\u3001B \u7528\u7ec6\u7ba1\u76f8\u8fde\uff0cA \u76db\u6709\u7406\u60f3\u6c14\u4f53\uff0cB \u4e3a\u771f\u7a7a\u3002\u6253\u5f00\u9600\u95e8\u8ba9\u6c14\u4f53\u81ea\u7531\u81a8\u80c0\u586b\u5145\u6574\u4e2a\u5bb9\u5668\uff0c\u8fbe\u5230\u5e73\u8861\u540e\u6e29\u5ea6\u5c06\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u7edd\u70ed\u81a8\u80c0\u82e5\u5bf9\u5916\u505a\u529f\u5219\u964d\u6e29\uff0c\u4f46\u5411\u771f\u7a7a\u81a8\u80c0\u4e0d\u514b\u670d\u4efb\u4f55\u963b\u529b\uff0c\u4e0d\u505a\u529f\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. \u964d\u4f4e<\/button>\r\n            <button onclick=\"handleExtremeAns(this, true, '\u6b63\u786e\uff01$Q=0, W=0$\uff0c\u7531\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\u77e5\u5185\u80fd $\\Delta U=0$\u3002\u7406\u60f3\u6c14\u4f53\u5185\u80fd\u53ea\u770b\u6e29\u5ea6\uff0c\u6545\u6e29\u5ea6\u4e0d\u53d8\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. \u4fdd\u6301\u4e0d\u53d8<\/button>\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u6c14\u4f53\u65e2\u6ca1\u6709\u5438\u70ed\u4e5f\u6ca1\u6709\u5f97\u5230\u5916\u754c\u505a\u529f\uff0c\u5185\u80fd\u548c\u6e29\u5ea6\u6ca1\u6709\u589e\u52a0\u7684\u673a\u5236\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. \u5347\u9ad8<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <div style=\"margin-bottom: 25px; padding: 20px; background: #f0f9ff; border-radius: 12px; border: 1px solid #e0f2fe;\">\r\n        <div style=\"display: flex; gap: 10px; margin-bottom: 15px;\">\r\n            <span style=\"background: #dcfce7; color: #166534 !important; padding: 2px 8px; border-radius: 4px; font-size: 12px; font-weight: bold; height: 20px; border: 1px solid #bbf7d0; flex-shrink: 0;\">Q3<\/span>\r\n            <p style=\"font-weight: 600; margin: 0; line-height: 1.5; color: #334155 !important;\">\u6c14\u7403\u5185\u538b\u5f3a\u964d\u81f3 $0.8P$\uff0c\u6e29\u5ea6\u964d\u81f3 $0.9T$\uff0c\u4f53\u79ef\u4e0d\u53d8\u3002\u5219\u9038\u51fa\u7684\u6c26\u6c14\u8d28\u91cf\u4e0e\u521d\u59cb\u603b\u8d28\u91cf\u4e4b\u6bd4\u4e3a\uff1a<\/p>\r\n        <\/div>\r\n        <div style=\"display: flex; flex-direction: column; gap: 10px;\">\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u8fd9\u4ec5\u8003\u8651\u4e86\u538b\u5f3a\u53d8\u5316\uff0c\u5ffd\u7565\u4e86\u6e29\u5ea6\u964d\u4f4e\u5bf9\u5bc6\u5ea6\u7684\u8865\u507f\u4f5c\u7528\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">A. 1 \/ 5<\/button>\r\n            <button onclick=\"handleExtremeAns(this, true, '\u6b63\u786e\uff01\u7531 $m \\propto P\/T$\uff0c\u5269\u4f59\u8d28\u91cf $m\\'\/m = 0.8\/0.9 = 8\/9$\u3002\u9038\u51fa\u6bd4\u4f8b\u4e3a $1 - 8\/9 = 1\/9$\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">B. 1 \/ 9<\/button>\r\n            <button onclick=\"handleExtremeAns(this, false, '\u9519\u8bef\u3002\u9038\u51fa\u91cf\u9700\u6839\u636e\u72b6\u6001\u65b9\u7a0b\u6bd4\u503c\u8ba1\u7b97\uff0c\u4e0d\u80fd\u76f4\u63a5\u7528\u6570\u503c\u76f8\u51cf\u3002')\" style=\"text-align: left; padding: 12px; border: 1px solid #cbd5e1; background: #ffffff !important; border-radius: 8px; cursor: pointer; font-size: 14px; transition: all 0.2s; color: #334155 !important; min-height: fit-content !important; line-height: 1.4 !important; display: block !important; width: 100% !important;\">C. 1 \/ 10<\/button>\r\n        <\/div>\r\n        <div class=\"ans-fb\" style=\"margin-top: 12px; font-size: 13px; display: none; padding: 12px; border-radius: 8px; line-height: 1.4;\"><\/div>\r\n    <\/div>\r\n\r\n    <script>\r\n    function handleExtremeAns(btn, isRight, info) {\r\n        const wrap = btn.parentElement;\r\n        const feedback = wrap.nextElementSibling;\r\n        const btns = wrap.querySelectorAll('button');\r\n        \r\n        btns.forEach(b => {\r\n            b.disabled = true;\r\n            b.style.cursor = 'default';\r\n            b.style.opacity = '0.5';\r\n        });\r\n\r\n        feedback.style.display = 'block';\r\n        feedback.textContent = info;\r\n\r\n        if (isRight) {\r\n            btn.style.setProperty('background', '#f0fdf4', 'important');\r\n            btn.style.setProperty('border-color', '#22c55e', 'important');\r\n            btn.style.setProperty('color', '#166534', 'important');\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#f0fdf4';\r\n            feedback.style.color = '#166534';\r\n            feedback.style.border = '1px solid #bbf7d0';\r\n        } else {\r\n            btn.style.setProperty('background', '#fef2f2', 'important');\r\n            btn.style.setProperty('border-color', '#ef4444', 'important');\r\n            btn.style.setProperty('color', '#991b1b', 'important');\r\n            btn.style.opacity = '1';\r\n            feedback.style.background = '#fef2f2';\r\n            feedback.style.color = '#991b1b';\r\n            feedback.style.border = '1px solid #fecaca';\r\n        }\r\n    }\r\n    <\/script>\r\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u4e00\u3001\u57fa\u7840 Q1 \u4e00\u5b9a\u8d28\u91cf\u7684\u7406\u60f3\u6c14\u4f53\uff0c\u5728\u4fdd\u6301\u4f53\u79ef\u4e0d\u53d8\u7684\u8fc7\u7a0b\u4e2d\uff0c\u82e5\u5176\u70ed\u529b\u5b66\u6e29\u5ea6\u5347\u9ad8\u4e3a\u539f\u6765\u7684 2 \u500d\uff0c\u5219\u6c14\u4f53\u7684\u538b\u5f3a\u53d8 &#8230; 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