A system absorbs `1000` cal of heat and does `1675J` work. If `J = 4.18 J//cal`, then find the change in internal energy of the system?

Explanation

To find the change in internal energy of 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-by-step Solution:

1. **Identify the given values:**
- Heat absorbed, \(Q = 1000 \, \text{cal}\)
- Work done, \(W = 1675 \, \text{J}\)
- Conversion factor, \(1 \, \text{cal} = 4.18 \, \text{J}\)

2. **Convert heat from calories to joules:**
\[ Q = 1000 \, \text{cal} \times 4.18 \, \text{J/cal} = 4180 \, \text{J} \]

3. **Substitute the values into the first law of thermodynamics equation:**
\[ \Delta U = Q - W \]
\[ \Delta U = 4180 \, \text{J} - 1675 \, \text{J} \]

4. **Calculate the change in internal energy:**
\[ \Delta U = 4180 \, \text{J} - 1675 \, \text{J} = 2505 \, \text{J} \]

Thus, the change in internal energy of the system is \(2505 \, \text{J}\).