Question

A gas is kept in a vessel of volume 0.2 m³ at temperature 300 K and pressure 1 bar. The molar heat capacity of gas at constant volume is 5 cal/mol K. The heat (kcal) required to raise the temperature to 400 K is ______.

Answer 1

Correct Answer: 4

Explanation:
Given:Molar specific heat at constant volume, $C_v=5cal/molK$The initial temperature of the gas, $T_1=300K$The final temperature of the gas, $T_2=400K$Volume of the gas, $V=0.2m^3$Pressure of the gas, $P=1$ bar $={10}^{5}N/m^2$Change in temperature,$\mathrm{\Delta }T=T_2-T_1=400K-300K=100K$Using the ideal gas equation,$PV=nRT\Rightarrow n=\frac{PV}{RT}$Where $n$ is the number of moles of the gas.Thus, the number of moles of gas at 1 atm is$n=\frac{(10{)}^5\times (0.2)}{8.31\times 300}$$\Rightarrow n\approx 8mol$The molar heat capacity of hydrogen at constant volume is$(\mathrm{\Delta }Q{)}_v=n{C}_v\mathrm{\Delta }T$$\Rightarrow (\mathrm{\Delta }Q{)}_v=8\times 5\times 100$$\Rightarrow (\mathrm{\Delta }Q{)}_v=4kcal$Thus, the heat required to raise the temperature to $400K$ is $4$ kcal. Hence, the correct answer is 4.