A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5 J and 8 J, respectively. Now gas is brought back to A by another process during which 3 J of heat is evolved. In this reverse process of B to A:

Options

A. 6 J of the work will be done by the gas
B. 6 J of the work will be done by the surrounding on gas
C. 10 J of the work will be done by the surrounding on gas
D. 10 J of the work will be done by the gas

Answer

To solve the problem step by step, we will analyze the changes in the gas's state and apply the first law of thermodynamics.

### Step 1: Understand the Process from A to B
- The gas absorbs heat (Q) and does work (W) during the transition from state A to state B.
- Given:
- Heat absorbed (Q) = +5 J (since heat is absorbed, it is positive)
- Work done by the gas (W) = -8 J (work done by the system is negative)

### Step 2: Calculate the Change in Internal Energy (ΔU) from A to B
- According to the first law of thermodynamics:
\[ \Delta U = Q + W \]
- Substituting the values:
\[ \Delta U = 5 \, \text{J} + (-8 \, \text{J}) = 5 \, \text{J} - 8 \, \text{J} = -3 \, \text{J} \]
- Thus, the change in internal energy from A to B is ΔU = -3 J.

### Step 3: Understand the Process from B to A
- The gas is brought back to state A from state B, during which heat is evolved.
- Given:
- Heat evolved (Q) = -3 J (since heat is released, it is negative)

### Step 4: Calculate the Change in Internal Energy (ΔU) from B to A
- We know from the previous step that ΔU from A to B was -3 J. For the reverse process (B to A), the change in internal energy will be the same in magnitude but opposite in sign:
\[ \Delta U = +3 \, \text{J} \]

### Step 5: Apply the First Law of Thermodynamics for the Process from B to A
- Again, using the first law:
\[ \Delta U = Q + W \]
- Substituting the values:
\[ 3 \, \text{J} = -3 \, \text{J} + W \]
- Rearranging gives:
\[ W = 3 \, \text{J} + 3 \, \text{J} = 6 \, \text{J} \]
- This means that 6 J of work is done on the gas by the surroundings.

### Step 6: Interpret the Result
- Since the work done (W) is positive, it indicates that the work is done on the gas by the surroundings.

### Conclusion
- The correct interpretation of the results is that 6 J of work is done on the gas by the surroundings.