Question

During an experiment, an ideal gas is found to obey a condition $\frac{P^2}{\rho }=constant(\rho =densityofthegas)$ The gas is initially at temperature T, pressurre P and density $\rho$. The gas expands such that density changes to $\rho /2$

• 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 proccess on P - T diagram is prabola
• D. The graph of the aobve process on P - T diagran 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 aobve process on P - T diagran is hyperbola.

Since $P^2=k\rho$, as ${\rho }^{\prime }=\rho /2$, $P^{\prime }=\frac{P}{\sqrt{2}}$

Also we can put $\rho =\frac{m}{V}$,

$⟹P^2=k\left(\frac{m}{V}\right)$

$⟹P^{2}V=mk=k^{\prime }$

we know that for an ideal gas $PV=nRT$,

Thus $P\left(nRT\right)=k^{\prime }$

$⟹PT=k^{\prime \prime }$ Thus a hyperbola of P-T curve.

$T\propto \frac{1}{P}$

$⟹T^{\prime }=\sqrt{2}T$