Volume versus temperature graphs for a given mass of an ideal gas… - Vidyadip

MCQ

Volume versus temperature graphs for a given mass of an ideal gas are shown in figure. At two different values of constant pressure. What can be inferred about relation between $P_1$ and $P_2$?

✓
$P_1 > P_2$
B
$P_{1}=P_2$
C
$P_1< P_2$
D
Data is insufficient.

✓

Answer

Correct option: A.

$P_1 > P_2$

$\text{V}\propto\text{T}$ as $n, R$ and $P$ are constant
$\frac{\text{V}_1}{\text{T}_1} =$ constant or slope of graph is constant
$\text{V}=\frac{\text{nRT}}{\text{P}}$
$\frac{\text{dv}}{\text{dt}}=\frac{\text{nR}}{\text{P}}$
so, $\frac{\text{dV}}{\text{dT}}$ increase when $P$ decreases
$\frac{\text{dV}}{\text{dT}}\alpha\frac{1}{\text{P}}$ as slope of $P_1$ is smaller than $P_2$.
Hence, $P_1 > P_2$ verifies option $(a).$

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