Physics

Problem

One mole of an ideal gas passes through a process where pressure and volume obey the relation

P = P_0 \left[ 1 - \frac{1}{2} \left( \frac{V_0}{V} \right)^2 \right]

. Here

P_0

and

V_0

are constants. Calculate the change in the temperature of the gas if its volume changes from

V_0

2V_0

. a.

\frac{1}{2} \frac{P_0 V_0}{R}

\frac{5}{4} \frac{P_0 V_0}{R}

\frac{3}{4} \frac{P_0 V_0}{R}

\frac{1}{4} \frac{P_0 V_0}{R}