QuestionAugust 11, 2025

When a fixed amount of ideal gas goes through an isochoric (constant volume) expansion, its pressure must increase its internal (thermal)energy does not change its temperature must increase no heat enters or leaves the gas the gas does no work

When a fixed amount of ideal gas goes through an isochoric (constant volume) expansion, its pressure must increase its internal (thermal)energy does not change its temperature must increase no heat enters or leaves the gas the gas does no work
When a fixed amount of ideal gas goes through an isochoric (constant volume) expansion, its pressure must increase its internal (thermal)energy does not change its temperature must increase no heat enters or leaves the gas the gas does no work

Solution
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Answer

Pressure must increase; internal energy changes; temperature must increase; heat enters the gas; no work is done. Explanation 1. Analyze Isochoric Process In an isochoric process, volume remains constant. According to the first law of thermodynamics, \Delta U = Q - W. Since volume is constant, W = 0. 2. Determine Pressure Change For ideal gases, pressure and temperature are directly related by **PV = nRT**. If volume is constant and temperature increases, pressure must increase. 3. Evaluate Internal Energy Change Internal energy change (\Delta U) for an ideal gas depends on temperature change. If temperature increases, internal energy increases. 4. Assess Heat Transfer Heat enters the system if temperature increases, as \Delta U = Q when W = 0. Therefore, heat must enter the gas. 5. Confirm Work Done No work is done since volume does not change (W = 0).

Explanation

1. Analyze Isochoric Process<br /> In an isochoric process, volume remains constant. According to the first law of thermodynamics, $\Delta U = Q - W$. Since volume is constant, $W = 0$.<br /><br />2. Determine Pressure Change<br /> For ideal gases, pressure and temperature are directly related by **$PV = nRT$**. If volume is constant and temperature increases, pressure must increase.<br /><br />3. Evaluate Internal Energy Change<br /> Internal energy change ($\Delta U$) for an ideal gas depends on temperature change. If temperature increases, internal energy increases.<br /><br />4. Assess Heat Transfer<br /> Heat enters the system if temperature increases, as $\Delta U = Q$ when $W = 0$. Therefore, heat must enter the gas.<br /><br />5. Confirm Work Done<br /> No work is done since volume does not change ($W = 0$).
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