The heat absorbed by a system in going through the given cyclic process is :

Heat and Thermodynamics PYQ — JEE Main 2024 · 5 Apr · Shift 1 · Q68 with Solution

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Correct answer: A

To find the heat absorbed in a cyclic process, we use the first law of thermodynamics.

1. Key idea for a cyclic process

For any cyclic process,

\Delta U = 0

because the system returns to its initial state.

Hence,

Q = W

So, the heat absorbed by the system is equal to the net work done in the cycle.

2. Work done in a cyclic process on a $P$ - $V$ diagram

The net work done in one complete cycle is equal to the area enclosed by the cycle on the $P$ - $V$ graph.

From the given figure, the enclosed area is triangular.

So,

W = \frac{1}{2} \times \text{base} \times \text{height}

Using the values from the graph:

Base $= 0.4\,\text{m}^3$
Height $= 308\,\text{N/m}^2$

Therefore,

W = \frac{1}{2} \times 0.4 \times 308

W = 0.2 \times 308 = 61.6\,\text{J}

3. Heat absorbed

Since for a cyclic process,

Q = W

we get

Q = 61.6\,\text{J}

4. Checking options

A: $61.6\,\text{J}$ ✅
B: $431.2\,\text{J}$ ❌
C: $19.6\,\text{J}$ ❌
D: $616\,\text{J}$ ❌

So, the correct answer is:

\boxed{61.6\,\text{J}}

More from Heat and Thermodynamics

2. Work done in a cyclic process on a

P

V

diagram

The net work done in one complete cycle is equal to the area enclosed by the cycle on the

P

V

graph.

From the given figure, the enclosed area is triangular.

So,

W = \frac{1}{2} \times \text{base} \times \text{height}

Using the values from the graph:

Base

= 0.4\,\text{m}^3

Height

= 308\,\text{N/m}^2

Therefore,

W = \frac{1}{2} \times 0.4 \times 308

W = 0.2 \times 308 = 61.6\,\text{J}

Heat and Thermodynamics question

Heat and Thermodynamics question

1. Key idea for a cyclic process

2. Work done in a cyclic process on a $P$ - $V$ diagram

3. Heat absorbed

4. Checking options

More from Heat and Thermodynamics

Heat and Thermodynamics question

Heat and Thermodynamics question

1. Key idea for a cyclic process

2. Work done in a cyclic process on a $P$ - $V$ diagram

3. Heat absorbed

4. Checking options

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1. Key idea for a cyclic process

2. Work done in a cyclic process on a PPP-VVV diagram

3. Heat absorbed

4. Checking options

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1. Key idea for a cyclic process

2. Work done in a cyclic process on a PPP-VVV diagram

3. Heat absorbed

4. Checking options

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2. Work done in a cyclic process on a $P$ - $V$ diagram

2. Work done in a cyclic process on a $P$ - $V$ diagram