What is `DeltaE` for system that does 500 cal of work on surrounding and 300 cal of heat is absorbed by the system ?

Options

A. `-200 cal`
B. `-300` cal
C. `+200` cal
D. `+300` cal

Explanation

To find the change in internal energy (ΔE) for the system, we will use the first law of thermodynamics, which states:

\[ \Delta E = Q - W \]

where:
- \( \Delta E \) is the change in internal energy,
- \( Q \) is the heat absorbed by the system,
- \( W \) is the work done by the system on the surroundings.

### Step-by-Step Solution:

1. **Identify the values given in the problem:**
- Work done by the system on the surroundings: \( W = 500 \, \text{cal} \) (since the system does work on the surroundings, this value is considered negative in our equation).
- Heat absorbed by the system: \( Q = 300 \, \text{cal} \) (since heat is absorbed, this value is positive).

2. **Assign the correct signs to the values:**
- Since the system does work on the surroundings, we take \( W = -500 \, \text{cal} \).
- The heat absorbed by the system is \( Q = +300 \, \text{cal} \).

3. **Substitute the values into the first law of thermodynamics equation:**
\[ \Delta E = Q - W \]
\[ \Delta E = 300 \, \text{cal} - (-500 \, \text{cal}) \]

4. **Simplify the equation:**
\[ \Delta E = 300 \, \text{cal} + 500 \, \text{cal} \]
\[ \Delta E = 800 \, \text{cal} \]

5. **Calculate the final value of ΔE:**
\[ \Delta E = 800 \, \text{cal} \]

### Final Answer:
The change in internal energy (ΔE) for the system is \( 800 \, \text{cal} \).