Question

For one mole of an ideal gas, the correct statement(s) is/are
[𝑈=internal energy; 𝑉= volume; 𝑇=temperature; 𝑃=pressure]

• A. \((\frac{∂U}{∂ V})_ T=0\)
• B. \((\frac{∂U}{∂ T})_ V>0\)
• C. \((\frac{∂P}{∂ T})_ V>0\)
• D. \((\frac{∂V}{∂ P})_ T>0\)

Answer 1

The Correct Option is A, B, C

• (A) This statement is true for an ideal gas. The internal energy of an ideal gas depends only on temperature, and for an ideal gas, \( \frac{\partial U}{\partial T}_V =0 \) since the energy is a function of temperature alone and not of volume.
• (B) This is incorrect because \(\frac{\partial U}{\partial T}_V =0\) for an ideal gas, meaning the internal energy does not increase with temperature for constant volume.
• (C) This is correct. The pressure of an ideal gas increases with temperature at constant volume, so \(\frac{\partial P}{\partial T}_V > 0\).
• (D) This is incorrect. The volume of an ideal gas depends inversely on pressure for a given temperature, so \( \frac{\partial V}{\partial P}_T < 0 \).

Thus, the correct answers are (A), (C).