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

Options

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

Explanation

To find the change in internal energy (ΔU) 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 1: Convert the heat absorbed from kcal to joules.
Given that the system has absorbed \( 2 \, \text{kcal} \) of heat, we need to convert this to joules. We know that:

\[ 1 \, \text{kcal} = 4184 \, \text{J} \]

Thus,

\[ Q = 2 \, \text{kcal} \times 4184 \, \text{J/kcal} = 8368 \, \text{J} \]

### Step 2: Identify the work done by the system.
The problem states that the system has done \( 500 \, \text{J} \) of work. In thermodynamics, work done by the system is considered as a positive quantity when calculating internal energy change.

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

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

\[ \Delta U = Q - W = 8368 \, \text{J} - 500 \, \text{J} \]

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

\[ \Delta U = 8368 \, \text{J} - 500 \, \text{J} = 7868 \, \text{J} \]

### Final Answer:
The change in internal energy of the system is \( 7868 \, \text{J} \).

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