In a thermodynamic process, pressure of a fixed mass of a gas is changed in such a manner that the gas release `20 J` of heat and `8 J` of work is done on the gas. If initial internal energy of the gas was `30 J`, what will be the final internal energy?

Options

A. 42 J
B. 18 J
C. 12 J
D. 60J

Answer

To find the final internal energy of the gas, we will use the first law of thermodynamics, which states:

\[ \Delta U = Q - W \]

Where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat added to the system,
- \(W\) is the work done by the system.

### Step 1: Identify the values given in the problem
- Heat released by the gas, \(Q = -20 \, \text{J}\) (since heat is released, it's negative)
- Work done on the gas, \(W = -8 \, \text{J}\) (since work is done on the system, it's negative)
- Initial internal energy, \(U_1 = 30 \, \text{J}\)

### Step 2: Substitute the values into the first law of thermodynamics
Using the formula:

\[ \Delta U = Q - W \]

Substituting the known values:

\[ \Delta U = (-20) - (-8) \]

### Step 3: Simplify the equation
This simplifies to:

\[ \Delta U = -20 + 8 = -12 \, \text{J} \]

### Step 4: Calculate the final internal energy
The change in internal energy is defined as:

\[ \Delta U = U_2 - U_1 \]

We can rearrange this to find \(U_2\):

\[ U_2 = U_1 + \Delta U \]

Substituting the values we have:

\[ U_2 = 30 + (-12) = 30 - 12 = 18 \, \text{J} \]

### Conclusion
The final internal energy of the gas is:

\[ \boxed{18 \, \text{J}} \]

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