Question

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

• A. $P_1<P_2$
• B. $P_1=P_2$
• C. data is insufficient.
• D. $P_1>P_2$

Answer 1

The correct option is D $P_1>P_2$

As we know, ideal gas equation is given by

$PV=nRT$ ...$\left(i\right)$

From the given equation, it shows $V\propto T$ as $n,R$ and $P$ are constant.

So,
$\frac{V}{T}=constant$

Therefore, from $\left(i\right)$ equation we have,

$V=\frac{nRT}{P}$ ...$\left(ii\right)$

Differentiate equation $\left(ii\right)$ with respect to $T$.

$\frac{dV}{dT}=\frac{nR}{P}$ ...$\left(iii\right)$

From equation $\left(iii\right)$ it shows,

Greater the magnitude of $\frac{dV}{dT}$
smaller will be the pressure values
Therefore,

$\frac{dV}{dT}\propto \frac{1}{P}$

Hence, it shows as slope of $P_1$ is smaller than $P_2,\text{so}{P}_1>P_2$.

$\text{Final Answer}:$ (𝑎).