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
$P_{M} V_{M}=\left(2 \times 10^{6}\right)(0.003)=6 \times 10^{3} \,J$
$P_{N} V_{N}=\left(0.8 \times 10^{6}\right)(0.005)=4 \times 10^{3} \,J$
$P_{M} V_{M} \neq P_{N} V_{N}$
Now, $\frac{P_{M} V_{M}}{T_{M}}=\frac{P_{N} V_{N}}{T_{N}}$ or $\frac{6 \times 10^{3} J }{T_{M}}=\frac{4 \times 10^{3} J }{T_{N}}$
$6 T_{N}=4 T_{M}$
$3 T_{N}=2 T_{M} \Rightarrow T_{M}=\frac{3}{2} T_{N}$
$T_{M}>\,T_{N}$