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

Question

Two different masses m and 3m of an ideal gas are heated separately in a vessel of constant volume, pressure P and absolute temperature T, graph for these two cases are shown in figure as A and B . The ratio of slope of curve B to A is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-k8k3ke6e9qmlw5py.jpg" /> (A) 3:1 (B) 1:3 (C) 9:1 (D) 1:9

Tardigrade Admin · Accepted Answer

PV=nRT PV=(m/M)⋅ RT <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-k8k3ke6e9qmlideh.jpg" /> A:(P/T)=(m/M)⋅ (R/V) B:(P/T)=(3 m/M)⋅ (R/V) (Slope of B/Slope of A)=(3/1)

Q. Two different masses $m$ and $3 m$ of an ideal gas are heated separately in a vessel of constant volume, pressure $P$ and absolute temperature $T,$ graph for these two cases are shown in figure as $A$ and $B$ . The ratio of slope of curve $B$ to $A$ is

$3 : 1$

$1 : 3$

$9 : 1$

$1 : 9$

$P V = n RT$
$P V = \frac{m}{M} \cdot RT$

$A : \frac{P}{T} = \frac{m}{M} \cdot \frac{R}{V}$
$B : \frac{P}{T} = \frac{3 m}{M} \cdot \frac{R}{V}$
$\frac{Sl o p eo f B}{Sl o p eo f A} = \frac{3}{1}$

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

3:1

1:3

9:1

1:9