One mole of an ideal monoatomic gas requires 200 J heat to increase its temperature by 10 K, when heated at constant pressure. The same gas is then heated at constant volume to increase its temperature by 10 K. What is the heat required ?

Options

A. 200 J
B. 300 J
C. 120 J
D. 80 J

Answer

C

Explanation

For a monoatomic gas, `C_(V)=(3R)/2andC_(P)=(5R)/2`
`dT=10K*n=1`
At constant volume, `(DeltaQ)_(V)=nC_(V)dT`
At constant pressure `(DeltaQ)_(P)=nC_(P)dT`
`therefore((DeltaQ)_(V))/((DeltaQ)_(P))=(nC_(V)dT)/(nC_(P)dT)=C_(V)/C_(P)=(3R)/2xx2/(5R)=3/5`
`therefore(DeltaQ)_(V)=3/5(DeltaQ)_(P)=3/5xx200=120J`