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  4. 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 />

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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
Question

NTA AbhyasNTA Abhyas 2022

Solution:

$PV=nRT$
$PV=\frac{m}{M}\cdot RT$
Solution
$A:\frac{P}{T}=\frac{m}{M}\cdot \frac{R}{V}$
$B:\frac{P}{T}=\frac{3 m}{M}\cdot \frac{R}{V}$
$\frac{Slope of \, B}{Slope of A}=\frac{3}{1}$