One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature diagram. The correct statement(s) is(are) :

Options

A. The above thermodynamic cycle exhibits only isochoric and adiabatc processes
B. The ratio of heat transfer during processes `1 to 2` and `3 to 4` is `|(Q_(1to2))/(Q_(3 to 4))|=1/2`
C. Work done in this thermodynamics cycle `(1 to 2 to 3 to 4 to 1)` is `|W| = 1/2 RT_0`
D. The ratio of heat transfer during processes `1 to 2` and `2 to 3` is `|(Q_(1to2))/(Q_(2 to 3))|=5/3`

Answer

C, D

Explanation

Process `1 to 2` and `3 to 4` are isobaric (as `V prop T`)
Process `2 to 3` and `4 to 1` are isochoric (as V is constant)`" ":." "`(A) is wrong
`Q_(1 to 2) = nC_p Delta T = nC_p (T_0)`
` Q_(3 to 4) = nC_p Delta T - n C_P (-T_0/2)`
`:." "|(Q_(1 to 2))/(Q_(3 to 4))|=2" ":." (B) is worng"`
`W_(1 to 2) = P Delta V = n R Delta T = nR(T_0)`
`W_(2 to 3) =0`
`W_(3to4) =0`
`:." Total work, "W = (nRT_0)/2 = (RT_0)/2" ":." (C) is correct "`
`Q_(1 to 2) = n C_P Delta T = nC_p (T_0)`
`Q_(2to3) = nC_V Delta T = nC_V (-T_0)`
`|(Q_(1 to 2))/Q_(2to3)|=C_p/C_V = 5/3" ":." (D) is correct"`