For a thermodynamic process `delta Q=- 50` calorie and `W =-20` calorie. If the nitial internal energy is `-30` calorie then final internal energy will be-

Options

A. 191.20 Calorie
B. `-60` Calorie
C. 100 Calorie
D. `– 100` Calorie

Answer

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

\[ \Delta Q = \Delta U + W \]

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

Given:
- \(\Delta Q = -50\) calories,
- \(W = -20\) calories,
- Initial internal energy \(U_{initial} = -30\) calories.

We need to find the final internal energy \(U_{final}\).

### Step 1: Rearranging the First Law of Thermodynamics

We can rearrange the first law equation to solve for the change in internal energy:

\[ \Delta U = \Delta Q - W \]

### Step 2: Substitute the Given Values

Now, substitute the given values into the equation:

\[ \Delta U = -50 - (-20) \]

### Step 3: Simplify the Equation

This simplifies to:

\[ \Delta U = -50 + 20 = -30 \text{ calories} \]

### Step 4: Calculate Final Internal Energy

Now, we can find the final internal energy using the change in internal energy:

\[ U_{final} = U_{initial} + \Delta U \]

Substituting the values:

\[ U_{final} = -30 + (-30) = -60 \text{ calories} \]

### Conclusion

Thus, the final internal energy \(U_{final}\) is \(-60\) calories.

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