Question

During an experiment, an 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 2V, then its temperature will be:

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

Answer 1

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

$P^{2}V=Constantor,{\left(\frac{RT}{V}\right)}^2.V=Constant[\because PV=RT]or,\frac{T^2}{V}=ConstantNow,T_1=T,V_1=V{T}_2=?,V_2=2V\therefore \frac{T_1^2}{V_1}=\frac{T_2^2}{V_2}\therefore T_2^2=\frac{V_2}{V_1}\times T_1^2=\frac{2V}{V}\times T^2\therefore T_2=\sqrt{2}T$