Question

For an adiabatic irreversible process involving an ideal gas:

• A. $\Delta U=n{C}_v\Delta T$
• B. $\Delta W=n{C}_v\Delta T$
• C. $W=-P_{ext.}(V_2-V_1)$
• D. $\Delta U=P_{ext.}(V_2-V_1)$

Answer 1

Answer: (A), (C), (D)

$\Delta U=P_{ext.}(V_2-V_1)$
$\Delta U=n{C}_v\Delta T$
$W=-P_{ext.}(V_2-V_1)$

An adiabatic process is one that occurs without the transfer of heat between a system and its surroundings; energy is transferred only as work.

For an adiabatic irreversible process involving an ideal gas, the correct statements are $\Delta U=n{C}_v\Delta T$ and $W=-P_{ext.}(V_2-V_1)$.

The equation $W=-P_{ext.}(V_2-V_1)$ refers to the work of expansion against constant external pressure.

Also, $\Delta U=\alpha nR\Delta T$ and $\alpha R=C_V$. Hence,$\Delta U=n{C}_v\Delta T$

Options A, C, and D are correct.