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

Question

Dr. Abubacker · Accepted Answer

(a) [image:13_image19.emf]
For a gas, $PV = \mu RT = \frac{m}{M}RT$
For graph $A,\ PV = \frac{m}{M}RT$
Slope of graph $A,$
$\left( \frac{P}{T} \right) = \frac{m}{M}\frac{R}{V}$ …(i)
For graph $B,\ PV = \frac{3m}{M}RT$
Slope of graph $B,$
$\left( \frac{P}{T} \right) = \frac{3m}{M}\frac{R}{V}$ …(ii)
$\frac{Slope\ of\ curve\ B}{Slope\ of\ curve\ A} = \frac{\frac{3m}{M}\frac{R}{V}}{\frac{m}{M}\frac{R}{V}} = \frac{3}{1}$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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