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 $A \to B$
Medium
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(b) Change in internal energy from $A \to B$ is
$\Delta U = \frac{f}{2}\mu R\Delta T = \frac{f}{2}({P_f}{V_f} - {P_i}{V_i})$
$ = \frac{3}{2}(2{P_0} \times 2{V_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.,
${W_{A \to B}} = \frac{1}{2}({P_0} + 2{P_0}) \times (2{V_0} - {V_0}) = \frac{3}{2}{P_0}{V_0}$
Hence, $\Delta Q = \Delta U + \Delta W$$ = \frac{9}{2}{P_0}{V_0} + \frac{3}{2}{P_0}{V_0} = 6{P_0}{V_0}$
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