A system absorbs 800 J of heat and system works equivalent to 900 J by expanding. The value of `Delta U` for the system is

Options

A. `-100` J
B. `-200` J
C. `-300` J
D. `-400` J

Answer

To find the change in internal energy (ΔU) for the system, we can 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 absorbed by the system,
- \( W \) is the work done by the system.

### Step 1: Identify the values of Q and W
- The system absorbs 800 J of heat, so:
\[ Q = +800 \, \text{J} \]
- The system does work equivalent to 900 J by expanding. Since this work is done by the system, it is considered negative:
\[ W = -900 \, \text{J} \]

### Step 2: Substitute the values into the equation
Now, we can substitute the values of \( Q \) and \( W \) into the first law equation:
\[ \Delta U = Q + W = 800 \, \text{J} + (-900 \, \text{J}) \]

### Step 3: Perform the calculation
Now, calculate \( \Delta U \):
\[ \Delta U = 800 \, \text{J} - 900 \, \text{J} = -100 \, \text{J} \]

### Final Result
The change in internal energy \( \Delta U \) for the system is:
\[ \Delta U = -100 \, \text{J} \]