Question

Which of the following isn’t correct for a fixed amount of ideal gas at constant volume?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

In case of an ideal Gas $PV=nRT$ say $n=1$

Then $PV=RT$, where $R$ is a constant and $V$ kept constant.
$PV=RTP=\left(\frac{R}{V}\right)T$
Taking the logarithm of the above equation
$\log \left(P\right)=\log \left(T\right)+\log \left(\frac{R}{V}\right)$
Here $R$ and $V$ are constant, then $\log \left(\frac{R}{V}\right)$ is constant and this will be intercept.

Again $\text{slope}=1\Rightarrow tan\theta =1\Rightarrow \theta ={45}^{\circ }$

According to Gay-lussac’s law, for a given mass of a gas the pressure ( P) is directly propertional to the absolute temperature at constant volume. So, the graph between pressure and temperature is a straight line passing through origin.

At constant volume, we know $PV=nRT\Rightarrow \frac{P}{T}=\frac{nR}{V}$

Hence the ratio of pressure and temperature is independent of temperature. So, the graph between $\frac{P}{T}$ vs $T$ will be a straight line parallel to $x-$axis.