Question

The following options represent the work done (W) and heat transfer (Q) relations for the various thermodynamic processes. Identify the INCORRECT option.
[Consider \( c_v, c_p \) - specific heats at constant volume and constant pressure respectively, \( p \)- pressure, \( v, v_1, v_2 \) - specific volumes of working fluid, \( T_1, T_2 \) - temperature at starting and end of the process.]

• A. Isochoric process \[ W = 0, \, Q = c_v (T_2 - T_1) \]
• B. Isobaric process \[ W = p(v_2 - v_1), \, Q = c_p (T_2 - T_1) \]
• C. Throttling process \[ W = 0, \, Q = 0 \]
• D. Isothermal process \[ W = 0, \, Q = p_1 v_1 \ln \left( \frac{T_1}{T_2} \right) \]

Hint:

In thermodynamic processes, pay attention to whether temperature, pressure, and volume are changing, as this will affect the work and heat transfer relations.

Answer 1

The Correct Option is D

In an isothermal process, the temperature remains constant, so the internal energy does not change. Therefore, for an ideal gas, the work done is equal to the heat transfer, and it should follow the relation \( Q = W = p_1 v_1 \ln \left( \frac{T_1}{T_2} \right) \). However, in this case, the work done should not be zero as implied in option (d). This makes option (d) the incorrect option.