What is the heat input needed to raise the temperature of 2 moles of helium gas from `0^@C` to `100^@C`
`(a) at constant volume,
(b) at constant pressure?
(c) what is the work done by the gas in part (b)?
Give your answer in terms of `R`.

Answer

A, B, C

Explanation

Helium is monoatomic gas. Therefore,
`C_gamma=(3R)/(2)` and `C_p=(5R)/(2)`
(a) At constant volume,
`Q=nC_VDeltaT`
`=(2)((3R)/(2))(100)`
`=300R`
(b) At constant pressure,
`Q=nC_pDeltaT`
`=(2)((5R)/(2))(100)`
`=500R`
(c) At constant pressure,
`W=Q-DeltaU`
`=nC_pDeltaT-nC_VDeltaT`
`=nRDeltaT=(2)(R)(100)`
`=200R`