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. $2.5 \, P_{0}V_{0}$
• B. $1.4 \, P_{0}V_{0}$
• C. $3.9 \, P_{0}V_{0}$
• D. $1.1 \, P_{0}V_{0}$

Answer 1

Answer: (C)

$Q_{A B}=\Delta U_{A B}+W_{A B}\Rightarrow W_{A B}=0$
$\Delta U_{A B}=\frac{f}{2}nR\Delta T\Rightarrow \frac{f}{2}\left(\Delta P V\right)$
$\Delta U_{A B}=\frac{5}{2}\left(\Delta P V\right)\Rightarrow Q_{A B}=2.5 \, P_{0}V_{0}$

Process BC
$Q_{B C}=\Delta U_{B C}+W_{B C}\Rightarrow Q_{B C}=0+2P_{0}V_{0}ln2=1.4 \, P_{0}V_{0}$
$Q_{n e t}=Q_{A B}+Q_{B C}=3.9 \, P_{0}V_{0}$