Question

During an experiment, an ideal gas is found to obey a condition $\frac{P^2}{\rho }$ $=$constant [$\rho =$density of the gas]. The gas is initially at temperature T, pressure P and density $\rho$. The gas expands such that density changes to $\frac{\rho }{2}$

• A. The pressure of the gas changes to $\sqrt{2}P$
• B. The temperature of the gas changes to $\sqrt{2}T$
• C. The graph of the above process on the P-T diagram is parabola.
• D. The graph of the above process on the P-T diagram is hyperbola.

Answer 1

Answer: (B), (D)

The correct options are
B The temperature of the gas changes to $\sqrt{2}T$
D The graph of the above process on the P-T diagram is hyperbola.

Equation of process $\Rightarrow \frac{P^2}{\rho }=$ constant $=C$ .... (1)
Equation of state $\Rightarrow \frac{P}{\rho }=\frac{R}{M}T$ .... (2)
From 1 and 2,

$PT=$ constant $\Rightarrow$ C is false, D is true.
Now, $\rho$-changes to $\frac{\rho }{2}\Rightarrow$ P changes to $\frac{P}{\sqrt{2}}$ from equation (1)
$\Rightarrow$ A is false.
Hence, T changes to $\sqrt{2}T\Rightarrow$ B is true