An amount `Q` of heat is added to a mono atomic ideal gas in a process in which the gas perfoms a work `Q//2` on its surrounding. Find equation of the process.

Explanation

From first law of thermodynamics, we have
`Q=DeltaU+W`
It is given that `W=Q/2`
Thus `Q=DeltaU+Q//2`
or `DeltaU=Q//2` …(3.75)
If C is the molar specific heat of the gas in this process then the amount of heat supplied can be given as
`Q=nCDeltaT` ...(3.76)
[If `DeltaT` is rise in temperature of gas ]
For change in internal energy of gas , we can write
`DeltaU=nC_V DeltaT`
or `=n((3R)/2)DeltaT` ..(3.77)
[As for a monoatom gas `C_V=((3R)/2)` ]
Thus from equation - (3.75), (3.76) and (3.77) we have
`nC_V DeltaT=1/2(nCDeltaT)`
or `C=2 C_V=3R`