Question

A fixed mass of ideal gas undergoes changes of pressure and volume starting at L, as shown in figure

Which graph shows how temperature (measured in Kelvin) changes with volume?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

IN $L$ to $M,$ pressure is constant so, $\frac{V}{T}=$ constant
$\Rightarrow T$ vs $V$ graph will be a straight line with some positive slope. $M$ to $N$ is not isothermal as
$P_M{V}_M=\left(2\times 10^6\right)(0.003)=6\times 10^{3}J$
$P_N{V}_N=\left(0.8\times 10^6\right)(0.005)=4\times 10^{3}J$
$P_M{V}_M\ne P_N{V}_N$
Now, $\frac{P_M{V}_M}{T_M}=\frac{P_N{V}_N}{T_N}$ or $\frac{6\times 10^{3}J}{T_M}=\frac{4\times 10^{3}J}{T_N}$
$6T_N=4T_M$
$3T_N=2T_M\Rightarrow T_M=\frac{3}{2}{T}_N$
$T_M>T_N$