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11.Thermodynamics
normal
The $P-V$ diagram of $2\,g$ 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
$4\,P_0V_0$
B
$6\,P_0V_0$
C
$4.5\,P_0V_0$
D
$2\,P_0V_0$
Solution
For Helium, degrees of freedom, $f=3$
Change in internal energy, $\Delta U=\frac{f}{2} \Delta(P V)$ $\Longrightarrow \Delta U=\frac{3}{2} \times\left(4 p_{o} V_{o}-p_{o} V_{o}\right)=\frac{9}{2} p_{o} V_{o}$
Work done by the gas is equal to the area under $P-V$ curve. Here, it is a trapezium under the curve.
$W=\frac{1}{2} V_{o}\left(p_{o}+2 p_{o}\right)=\frac{3}{2} p_{o} V_{o}$
From first law of thermodynamics, total heat given is$:$
$\Delta Q=W+\Delta U$
$\Delta Q=\frac{3}{2} p_{o} V_{o}+\frac{9}{2} p_{o} V_{o}$
$\Delta Q=6 p_{o} V_{o}$
Standard 11
Physics
