A system absorbs 50 kJ heat and does 20 kJ of work. What is the net change in the internal energy of the system ?

Options

A. Increase by 30 kJ
B. Decrease by 30 kJ
C. Increase by 70 kJ
D. Decrease by 70 kJ

Explanation

To find the net change in the internal energy of the system, we will use the first law of thermodynamics, which is expressed as:

\[ \Delta U = Q + W \]

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 of Q and W
In this problem:
- The system absorbs 50 kJ of heat, so \(Q = +50 \, \text{kJ}\).
- The system does 20 kJ of work, which means it is expending energy. Therefore, in thermodynamic terms, the work done by the system is negative, so \(W = -20 \, \text{kJ}\).

### Step 2: Substitute the values into the equation
Now, we substitute the values of \(Q\) and \(W\) into the first law of thermodynamics equation:

\[ \Delta U = Q + W = 50 \, \text{kJ} + (-20 \, \text{kJ}) \]

### Step 3: Perform the calculation
Now, we perform the addition:

\[ \Delta U = 50 \, \text{kJ} - 20 \, \text{kJ} = 30 \, \text{kJ} \]

### Conclusion
The net change in the internal energy of the system is:

\[ \Delta U = +30 \, \text{kJ} \]