`C_p` is always greater than `C_v` for a gas, which of the following statements provide, partly or wholly, the reason for this?
(i) No work is done by a gas at constant volume
(ii) When a gas absorbs heat at constant pressure, its volume must change
(iii) For the same change in temperature, the internal energy of a gas changes by a smaller amount at constant volume that at constant pressure
(iv) The internal energy of an ideal gas is a function only of its temperature

Options

A. (i),(ii)
B. (ii),(iii)
C. (iii),(iv)
D. all

Answer

A

Explanation

When heat `Q` is supplied at constant volume
`Q=Q_V=DeltaU=nC_VDeltaT` .(i)
When heat Q is supplied at constant pressure
`Q=Q_P=DeltaU'+DeltaW=nC_V(DeltaT)'+DeltaW`
`C_V=(1)/(n)(Q)/(DeltaT)`
`C_P=(1)/(n)(1)/((DeltaT)')`
`(DeltaT)' lt (DeltaT)`, hence, `C_p gt C_V`