Question

The $p-V$ diagram of $2g$ 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 $6p_0{V}_0$

For Helium, degrees of freedom, $f=3$

Change in internal energy, $\Delta U=\frac{f}{2}\Delta \left(PV\right)$

$⟹\Delta U=\frac{3}{2}\times (4p_o{V}_o-p_o{V}_o)=\frac{9}{2}{p}_o{V}_o$

Work done by the gas is equal to the area under $P-V$ curve. Here, it is a trapezium under the curve.

$W=\frac{1}{2}{V}_o(p_o+2p_o)=\frac{3}{2}{p}_o{V}_o$

From first law of thermodynamics, total heat given is:

$\Delta Q=W+\Delta U$

$\Delta Q=\frac{3}{2}{p}_o{V}_o+\frac{9}{2}{p}_o{V}_o$

$\Delta Q=6p_o{V}_o$