One mole of an ideal monoatomic gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is [Given the gas constant R = 8.3 J/ mol. K]

Options

A. 198.7 J
B. 29 J
C. 215.3 J
D. 124 J

Answer

D

Explanation

`(Delta Q) _(P) = mu C_(p)Delta T implies 207 = 1 xx C_(p) xx10`
`implies C_(P) = 20.7 (" joule")/(mol -K)`Also `C_(P)-C_(V)=R`
`implies C_(V)=c_(P)-R=20.7-8.3 =12.4 ("Joule")/("mole"-K)`
SO ` (Delta Q) _(V) = mu C_(v) Delta t=1xx12.4 xx10=124J`