Question

For an ideal gas:
(1) the change in internal energy in a constant pressure process from temperature $T_1$ and $T_2$ is equal to $n{C}_V\left(T_2-T_1\right)$ where $C_V$ is the molar heat capacity at constant volume and $n$ the number of moles of the gas
(2) the change in internal energy of the gas and work done by the gas are equal in magnitude in an adiabatic process
(3) the internal energy increases in an isothermal process
(4) no heat is added or removed in an adiabatic process

• A. 1 and 2 are correct
• B. 2 and 3 are correct
• C. 1 and 4 and correct
• D. 1, 2 and 4 are correct

Answer 1

Answer: (D)

1. $\Delta U=n{C}_V\Delta T=n{C}_V\left(T_2-T_1\right)$ in all processes.
2. In adiabatic process, $\Delta Q=\theta$
From 1st law of thermodynamics
$\Delta Q=\Delta U+\Delta W$
$\Rightarrow \Delta U=-\Delta W$
$\Rightarrow |\Delta U|=|\Delta W|$
3 . In isothermal process $\Delta T=0$
$\therefore \Delta U=0$ (as $\Delta U=n{C}_V\Delta T$ )
4 . In adiabatic process, $\Delta Q=0$, ie.,
in adiabatic process, no heat is added or removed into or out of the system.