When the state of a gas adiabatically changed from an equilibrium state A to another equilibrium state B an amount of work done on the stystem is 35 J. If the gas is taken from state A to B via process in which the net heat absorbed by the system is 12 cal, then the net work done by the system is (1 cal = 4.19 J)

Options

A. a. 13.2J
B. b. 15.4 J
C. c. 12.6 J
D. d. 16.8 J

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Work Done on the System
When the gas changes from state A to state B adiabatically, the work done on the system is given as 35 J. Since work is done on the system, we consider this as negative work done by the system. Thus, we can write:
\[ W_{on} = -35 \, \text{J} \]

### Step 2: Calculate Change in Internal Energy (ΔU)
For an adiabatic process, the change in internal energy (ΔU) is equal to the negative of the work done on the system:
\[ \Delta U = -W_{on} = -(-35 \, \text{J}) = 35 \, \text{J} \]

### Step 3: Convert Heat Absorbed from Calories to Joules
The problem states that the net heat absorbed by the system during the process is 12 cal. We need to convert this to joules using the conversion factor \(1 \, \text{cal} = 4.19 \, \text{J}\):
\[ Q = 12 \, \text{cal} \times 4.19 \, \text{J/cal} = 50.28 \, \text{J} \]

### Step 4: Apply the First Law of Thermodynamics
According to the first law of thermodynamics:
\[ \Delta U = Q + W \]
Where:
- \( \Delta U \) is the change in internal energy,
- \( Q \) is the heat absorbed,
- \( W \) is the work done by the system.

We can rearrange this equation to find the work done by the system:
\[ W = \Delta U - Q \]

### Step 5: Substitute the Values
Now we can substitute the values we have calculated:
- \( \Delta U = 35 \, \text{J} \)
- \( Q = 50.28 \, \text{J} \)

Thus,
\[ W = 35 \, \text{J} - 50.28 \, \text{J} = -15.28 \, \text{J} \]

### Step 6: Conclusion
The net work done by the system when it is taken from state A to state B via the process in which the net heat absorbed is 12 cal is:
\[ W \approx -15.28 \, \text{J} \]