Two moles of ideal helium gas are in a rubber balloon at `30^@C.` The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to `35^@C.` The amount of heat required in raising the temperature is nearly (take R
`=8.31 J//mol.K`)

Options

A. `62 J`
B. `104 J`
C. `124 J`
D. `208 J`

Answer

D

Explanation

Here, `n=2, T_(1)= 30^(@)C, T_(2)= 35^(@)C`
`R=8.31J//mol e K, dQ=?`
As the gas in ballon is expanding at constant pressure, therefore, `dQ= nC_(p)dT`
Helium is monoatomic gas with `C_(p)= 5/2R`
`:. dQ= 2xx5/2R(T_(2)-T_(1))= 5R(T_(2)-T_(1))`
`=5xx8.31(35-30)= 207.75~~208 J`