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

Options

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

Explanation

To find the internal energy change in 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 kilocalories to joules
The problem states that the system has absorbed \( 2 \) kilocalories of heat. We need to convert this to joules.

1 kilocalorie = 1000 calories
1 calorie = 4.2 joules

So,
\[ Q = 2 \text{ kcal} = 2 \times 1000 \text{ cal} = 2000 \text{ cal} \]
\[ Q = 2000 \text{ cal} \times 4.2 \text{ J/cal} = 8400 \text{ J} \]

### Step 2: Identify the work done
The problem states that the work done by the system is \( 500 \) joules. Since the work is done by the system, we will consider it as positive in our equation.

\[ W = 500 \text{ J} \]

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

\[ \Delta U = Q - W \]
\[ \Delta U = 8400 \text{ J} - 500 \text{ J} \]
\[ \Delta U = 7900 \text{ J} \]

### Conclusion
The change in internal energy of the system is \( 7900 \) joules.

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