# GATE2018-50

$$P\left ( V-nb \right )=nRT$$
where $b=0.029\:m^{3}$/mol. The temperature and volume are $500 \:^{\circ}C$ and $5\:m^{3}$ respectively for $100$ moles of methane. At this state of the system, the isobaric rate of change of temperature with volume (in $^{\circ}C\:/m^{3}$) is ________________ (rounded off to second decimal place).