Three moles of an ideal gas `(C_p=7/2R)` at pressure `p_0` and temperature `T_0` is isothermally expanded to twice its initial volume. It is then compressed at a constant pressure to its original volume.
(a) Sketch p-V and p-T diagram for complete process.
(b) Calculate net work done by the gas.
(c) Calculate net heat supplied to the gas during complete process.
(Write your answer in terms of gas constant =R)

Answer

A, B, C, D

Explanation

(a)
For the process AB,
`(p_0V_0)/(T_0)=(p_B(2V_0))/(T_0)`
`:.` `p_B=p_0/2`
`DeltaU=0`
`Q=W+DeltaU`
`=nRTInV_B/V_A`
`=3RT_0In2`
For the process BC,
`(2V_0)/(T_0)=V_0/T_C`
`:.` `T_C=T_0/2`
`W=nRDeltaT=3R(T_0/2-T_0)=-3/2RT_0`
`Q=nC_pDeltaT=-21/4RT_0`
`:.` `W_(Total)=3RT_(0)In(2)-3/2RT_0`
(c) `Q_(Total)=3RT_(0)In(2)-21/4RT_0`