BITSAT 2024 Shift 1 Paper

In the cycle A⟶B⟶C⟶D⟶A, heat is added to the system during the processes D⟶A (at constant volume) and A⟶B (at constant pressure).
Calculating the Heat Added
Heat for Process D⟶A (Constant Volume):
For an ideal monoatomic gas, the molar heat capacity at constant volume CV is given by:
CV=‌

3

2

R
The heat added during this process is:
QDA=nCV(∆T)DA=‌

3

2

nR∆T
Heat for Process A⟶B (Constant Pressure):
The molar heat capacity at constant pressure Cp is given by:
Cp=‌

5

2

R
The heat added during this process is:
QAB=nCp(∆T)AB=‌

5

2

nR∆T
Total Heat Supplied

The total heat supplied in the cycle is the sum of the heat added during these two processes:
Q=QDA+QAB
Substitute the expressions for QDA and QAB :
Q=‌

3

2

nR∆T+‌

5

2

nR∆T
Given nR∆T=p∆V, and substituting it:
Q=‌

3

2

(p0V0)+‌

5

2

(p0V0)
This simplifies to:
Q=‌

13

2

p0V0