310 J of heat is required to rise the temperature of 2 moles of an ideal gas at constant pressure from `25^(@)C` to `35^(@)C`. The amount of heat required to raise the temperature of the gas through the same range at constant volume, is

Options

A. 384 J
B. 144 J
C. 276 J
D. 452 J

Answer

B

Explanation

At constant pressure,
Heat required `=nC_(p)DeltaT`
`rArr" " 310=2xxC_(p)xx(35-25)`
`rArr" " C_(p)=(310)/(20)=15.5J "mol" ^(-1)K^(-1)`
Similarly ,at constant volume ,
Heat required `nC_(v)DeltaT`
`=2(C_(p)-R)xx(35-25)" " [becauseC_(p)-C_(v)=R] `
`=2xx(15.5-8.3)xx10`
`=2xx7.2xx10=144 J`