The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PV-diagram with `P_0 V_0 = 1/3, RT_0` , the correct match is :

Options

A. `I to Q, II to R, III to S , IV to U`
B. `I to Q , II to R, III to S , IV to U`
C. `I to Q, II to S, III to R , IV to U`
D. `I to S , II to S, III to Q , IV to T`

Answer

B

Explanation

`1 to 2` Isothermal process
`2 to 3` Isochoric process
`W_(1 to 2 to 3) = W_(1to2) =P_0 (2V_0 -V_0) = P_0 V_0 =(RT_0)/3`
`U_(1 to 2 to 3) = U_(1 to 2 ) +U_(2 to 3)`
` = 3/2 [P_2 V_2 - P_1 V_1 ] +3/2[P_3 V_3- P_2 V_2] =3/2 P_0 [2 V_0 - V_0]+3/2 [(3p_0)/2 xx2V_0 -p_0 (2 V_0)]`
`=3/2 P_0 V_0 + 3/2 P_0 V_0 = 3 P_0 V_0 = 3xx(RT_0)/3 = RT_0`
`Q_(1 to 2 to 3) = Q_(1to 2)+ Q_(2 to 3)`
`W_(1 to 2) + Delta u_(1 to2 ) + Delta u_(2 to 3) P_0 V_0 +3/2 P_0 V_0 + 3/2 P_0 V_0 = 4 P_0 V_0 = (4 RT_0)/3`
`Q_(1 to 2)= 5/2 P_0 V_0 = 5/6 RT_0`
Correct option is (B)