Two different masses `m` and `3 m` 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

Options

A. `3:1`
B. `1:3`
C. `9:1`
D. `1:9`

Answer

A

Explanation

Slope of line passing through origin on `P-T` diagram
Slope of B: `((P)/(T))_B=(nR)/(V)=(((3m)/(M_0))R)/(V)`
Slope of A: `((P)/(T))_A=(n'R)/(V)=(((m)/(M_0))R)/(V)`
`(((P)/(T))_B)/(((P)/(T))_A)=(3m)/(m)=(3)/(1)`