Select the correct alternatives for an ideal gas :

Options

A. The change in internal energy in a constant pressure process from trmperature `T_(1)` to `T_(2)` is equal to `nC_(v) (T_(2)-T_(1))` , where `C_(v)` is the molar specific heat at constant volume and `n` the number of moles of the gas.
B. The change in internal energy of the gas and the work done by the gas are equal in magnitude in an adiabatic process.
C. The internal energy does not chagne in an isothermal process.
D. No heat is addes or removed in an adiabatic process.

Answer

A, B, C, D

Explanation

(a)`DeltaU=Q-W=nC_(p)DeltaT-PDeltaV`
`= n C _(p)Delta T-nRDeltaT=n(C_(p)-R)DeltaT`
`=nC_(v)DeltaT=nC_(v)(T_(2)-T_(1))`
`(b)` `DeltaQ=DeltaU+DeltaW`
But `DeltaQ=0` for adiabatic process, hence
`DeltaU=- DeltaW`
or, `|DeltaU|=|Delta W|`
`(c)` `DeltaU=n C_(v) Delta T =0 ` `( :. DeltaT=0)`
`(d)` `DeltaQ=0 (` in adiabatic change `)`