Heat given to a system is 35 joules and work done by the system is 15 joules. The change in the internal energy of the system will be

Options

A. -50J
B. 20 J
C. 30 J
D. 50 J

Answer

To find the change in internal energy of the system, we can use the first law of thermodynamics, which is given by the equation:

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

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

### Step-by-Step Solution:

1. **Identify the given values:**
- Heat given to the system, \(\Delta Q = 35 \, \text{joules}\)
- Work done by the system, \(W = 15 \, \text{joules}\)

2. **Substitute the known values into the first law of thermodynamics equation:**
\[ 35 = \Delta U + 15 \]

3. **Rearrange the equation to solve for \(\Delta U\):**
\[ \Delta U = 35 - 15 \]

4. **Calculate \(\Delta U\):**
\[ \Delta U = 20 \, \text{joules} \]

Thus, the change in the internal energy of the system is \(20 \, \text{joules}\).

### Final Answer:
\(\Delta U = 20 \, \text{joules}\)

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