Two moles of an ideal monoatomic gas occupies a volume V at 27^@ C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change on its internal energy.

Two moles of an ideal monoatomic gas occupies a volume V at 27^@ C. Th

1.	Two moles of an ideal monoatomic gas occupies a volume V at 27^@ C. The gas expands adiabatically to a volume 2 V. Calculate (a) the final temperature of the gas and (b) change on its internal energy.
Answer» (a)189 K (b)2.7 kJ (a)195 K (b)-2.7 kJ (a)189 K (b)-2.7 kJ (a)195 K (b)2.7 kJ Solution :For adiabatic CHANGE , `PV^gamma` =constant and equation of state of gas `PV=muRT` `therefore (PV^gamma)/(PV)="constant"/(muRT)` `therefore V^(gamma-1) = "constant"/T` [`because mu R`= constant] `therefore V^(gamma-1) PROP 1/T` `therefore (V_1/V_2)^(gamma-1)=T_2/T_1` `therefore T_2=T_1xx(V_1/V_2)^(gamma-1)` `=300xx(1/2)^(5/3-1)` `=300xx(0.5)^(2/3)` =189 K Change in internal energy , `DeltaU=(mu f R DeltaT)/2` `=2xx3/2xx8.314xx(189-300)` =3 x 8.314 x (-111) =- 333 x 8.314 =-2768 J `therefore DeltaU APPROX` -2.7 KJ (almost near value)