In changing the state of a gas adiabatically from an equilibrium state A to another equilibrium state B an amount of work equal to 22.3 J is done on the system.If the gas is taken from state A to B via a process in which the net heat absorbed by the system is 9.35 cal then the net work done by the system in latter case is
(Take 1 case =4.2 J)

Options

A. 15 J
B. 16 J
C. 17 J
D. 18 J

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Information
We are given:
- Work done on the system during an adiabatic process from state A to B, \( W_{adiabatic} = -22.3 \, J \) (negative because work is done on the system).
- Heat absorbed by the system in a different process from A to B, \( Q = 9.35 \, cal \).

### Step 2: Convert Heat from Calories to Joules
We need to convert the heat absorbed from calories to joules using the conversion factor \( 1 \, cal = 4.2 \, J \):
\[ Q = 9.35 \, cal \times 4.2 \, \frac{J}{cal} = 39.27 \, J \]

### Step 3: Determine the Change in Internal Energy
In the adiabatic process, the change in internal energy \( \Delta U \) is equal to the negative of the work done on the system:
\[ \Delta U = -W_{adiabatic} = -(-22.3 \, J) = 22.3 \, J \]

### Step 4: Apply the First Law of Thermodynamics
According to the first law of thermodynamics:
\[ \Delta Q = \Delta U + W \]
We can rearrange this to find the work done in the latter process:
\[ W = \Delta Q - \Delta U \]

### Step 5: Substitute the Values
Now we can substitute the values we have:
\[ W = 39.27 \, J - 22.3 \, J \]
\[ W = 16.97 \, J \]

### Step 6: Round the Result
Rounding 16.97 J gives us approximately:
\[ W \approx 17 \, J \]

### Final Answer
The net work done by the system in the latter case is approximately **17 J**.

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