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

Explanation:
Given:Molar specific heat at constant volume, Cv=5cal/molKThe initial temperature of the gas, T1=300 KThe final temperature of the gas, T2=400 KVolume of the gas, V=0.2 m3Pressure of the gas, P=1 bar =105 N/m2Change in temperature,ΔT=T2−T1=400K−300K=100KUsing the ideal gas equation,PV=nRT⇒n=PVRTWhere n is the number of moles of the gas.Thus, the number of moles of gas at 1 atm isn=(10)5×(0.2)8.31×300⇒n≈8molThe molar heat capacity of hydrogen at constant volume is(ΔQ)v=nCvΔT⇒(ΔQ)v=8×5×100⇒(ΔQ)v=4kcalThus, the heat required to raise the temperature to 400 K is 4 kcal. Hence, the correct answer is 4.