Question

During an experiment, ideal gas obeys an addition equation of state $P^{2}V=constant$. The initial temperature and pressure of the gas are $T$ and $V$ respectively. When it expands to volume 2$V$, then its temperature will be:

• A. $T$
• B. $\sqrt{2}$
• C. $2T$
• D. $\sqrt{2}T$

Answer 1

The correct option is D $\sqrt{2}T$

Ideal gas equation $PV=nRT$.
Initial position: $P=P_1,V=V_1,T=T_1$
Final position: $P=P_2,V=V_2=2V_1,T=T_2$
As volume doubles, $P_2=\left(P_1/\sqrt{2}\right)$ according to $P^{2}V=constant$.
So $\frac{P_1{V}_1}{P_2{V}_2}=\frac{T_1}{T_2}$,$T_2=\sqrt{2}{T}_1$.