At `27^@C` two moles of an ideal monatomic gas occupy a volume V. The gas expands adiabatically to a volume `2V`. Calculate
(a) final temperature of the gas
(b) change in its internal energy and
(c) the work done by the gas during the process. [ `R=8.31J//mol-K`]

Explanation

Using (a) `T_(2)V_(2)^((gamma-1))=T_(1)V_(1)^((gamma-1))`
`T_(2)=T_(1)(V_(1)/(V_(2)))^((gamma-1))= 300(1/2)^((5//3-1))=189K`
(b) `dU= (n) C_((v))DeltaT=(nRDeltaT)/(gamma-1)= 2xx3/2xx8.31(189-300)= 276.23J`
(c )As `dQ=0=dU+dW :. dW= -dU= 2767.23J`