Question

An ideal diatomic gas undergoes a thermodynamic process as shown in the $P-V$ diagram. The process $AB$ is isochoric while the process $BC$ is isothermal. The total heat given to the gas in the process is nearly (use $ln2=0.7$ )

• A. $2.5P_0{V}_0$
• B. $1.4P_0{V}_0$
• C. $3.9P_0{V}_0$
• D. $1.1P_0{V}_0$

Answer 1

Answer: (C)

$Q_{AB}=\Delta U_{AB}+W_{AB}\Rightarrow W_{AB}=0$
$\Delta U_{AB}=\frac{f}{2}nR\Delta T\Rightarrow \frac{f}{2}\left(\Delta PV\right)$
$\Delta U_{AB}=\frac{5}{2}\left(\Delta PV\right)\Rightarrow Q_{AB}=2.5P_0{V}_0$

Process BC
$Q_{BC}=\Delta U_{BC}+W_{BC}\Rightarrow Q_{BC}=0+2P_0{V}_{0}ln2=1.4P_0{V}_0$
$Q_{net}=Q_{AB}+Q_{BC}=3.9P_0{V}_0$