The internal energy change in a system that has absorbed `2 kcal` of heat and done `500J` of work is

Options

A. 8900 J
B. 6400 J
C. 5400 J
D. 7900 J

Answer

To find the internal energy change in 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, and
- \(W\) is the work done by the system.

### Step 1: Identify the given values
- Heat absorbed (\(Q\)) = 2 kcal
- Work done (\(W\)) = 500 J

### Step 2: Convert heat absorbed from kcal to joules
We know that:
1 kcal = 1000 calories
1 calorie = 4.2 joules

Therefore:
\[ Q = 2 \text{ kcal} = 2 \times 1000 \text{ calories} = 2000 \text{ calories} \]
\[ Q = 2000 \text{ calories} \times 4.2 \text{ J/calorie} = 8400 \text{ J} \]

### Step 3: Substitute the values into the formula
Now we can substitute \(Q\) and \(W\) into the equation:
\[ \Delta U = Q - W \]
\[ \Delta U = 8400 \text{ J} - 500 \text{ J} \]

### Step 4: Calculate the change in internal energy
\[ \Delta U = 7900 \text{ J} \]

### Conclusion
The internal energy change in the system is \(7900 \text{ J}\).

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