Question

The P-V diagram of 2 gm of helium gas for a certain process A $\to$ B is shown in the figure. what is the heat given to the gas during the process A $\to$ B

• A. $4P_0{V}_0$
• B. $6P_0{V}_0$
• C. $4,5P_0{V}_0$
• D. $2P_0{V}_0$

Answer 1

The correct option is B $6P_0{V}_0$

Change in internal energy from $A\to B$
$△U=\frac{f}{2}\mu R△T=\frac{f}{2}(P_f{V}_f-P_i{V}_i)$
$=\frac{3}{2}(2P_0\times 2V_0-P_0\times V_0)=\frac{9}{2}{P}_0{V}_0$
work done in process $A\to B$ is equal to the area covered by the graph
with volume axis i.e.,
$W_{A\to B}=\frac{1}{2}(P_0+2P_0)\times (2V_0-V-0)=\frac{3}{2}{P}_0{V}_0$
$Hence,△Q=△U+△W=\frac{9}{2}{P}_0{V}_0+\frac{3}{2}{P}_0{V}_0=6P+0V_0$