T-V diagram of two moles of a monoatomic gas is as shown in figure.
For the process abcda choose the correct options given below

Options

A. (a) `DeltaU=0`
B. (b) work done by gasgt0
C. (c) heat given to the gas is `4RT_0`
D. (d) heat given to the gas is `2RT_0`

Answer

A, B

Explanation

ab `W=0` (as V= constant )
`Q_1=DeltaU_1=nC_VDeltaT`
`=(2)(3/2R)(2T_0-T_0)=3RT_0`
bc `DeltaU=0` (as T=constant)
`:.` `Q_2=W_2=nRT In(V_f/V_i)`
`=(2)(R)(2T_0) In(2)`
`=4RT_0 In(2)`
cd `W=0`
`Q_3=DeltaU_3=nC_VDeltaT`
`(2)(3/2R)(T_0-2T_0)`
`=-3RT_0`
da `DeltaU=0`
`Q_4=W_4=nRT In((V_f)/(V_i))`
`=(2)(R)(T_0) In(1/2)`
`=-2RT_(0) In(2)`
Now in complete cycle,
`DeltaU_(n et)=0`
`Q_(n et)=W_(n et)=2RT_(0) In(2)=+ve`