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 will 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: Convert heat absorbed from calories to joules.
We are given that the system absorbs \(1000\) cal of heat. We need to convert this to joules using the conversion factor \(1 \text{ cal} = 4.18 \text{ J}\).

\[ Q = 1000 \text{ cal} \times 4.18 \text{ J/cal} = 4180 \text{ J} \]

### Step 2: Identify the work done by the system.
The work done by the system is given as \(W = 1675 \text{ J}\).

### Step 3: Substitute the values into the first law of thermodynamics equation.
Now, we can substitute the values of \(Q\) and \(W\) into the equation:

\[ \Delta U = Q - W = 4180 \text{ J} - 1675 \text{ J} \]

### Step 4: Calculate the change in internal energy.
Now, we perform the subtraction:

\[ \Delta U = 4180 \text{ J} - 1675 \text{ J} = 2505 \text{ J} \]

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

\[ \Delta U = 2505 \text{ J} \]

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