Question

Two different masses m and 3m of an ideal gas are heated separately in a vessel of constant volume, the pressure P and absolute temperature T, graphs for these two cases are shown in the figure as A and B. The ratio of slopes of curves B to A is -

• A. 3:1
• B. 1:3
• C. 9:1
• D. 1:9

Answer 1

The correct option is A 3:1


For a gas, $PV=\mu RT=\frac{m}{M}RT$
For graph A, $PV=\frac{m}{M}RT$
Slope of graph A, $\frac{P}{T}=\frac{m}{M}\frac{R}{V}$ ...(1)
For graph B, $PV=\frac{3m}{M}RT$
Slope of graph B,$\frac{P}{T}=\frac{3m}{M}\frac{R}{V}$
$\frac{\text{Slope of curve B}}{\text{Slope of curve A}}=\frac{\frac{3m}{M}\frac{R}{V}}{\frac{m}{M}\frac{R}{V}}=\frac{3}{1}$