Calculate the increase in internal energy of system when 40 joule heat is supplied and the work done by a system is 8 joule

Options

A. 25 J
B. 30 J
C. 32 J
D. 28 J

Answer

To calculate the increase in internal energy of the system, we can use the first law of thermodynamics, which is expressed as:

\[ Q = \Delta U + W \]

Where:
- \( Q \) is the heat supplied to the system.
- \( \Delta U \) is the change in internal energy of the system.
- \( W \) is the work done by the system.

### Step 1: Identify the values given in the problem
- Heat supplied, \( Q = 40 \) joules
- Work done by the system, \( W = 8 \) joules (Note: Since the work is done by the system, it will be considered as positive in the equation.)

### Step 2: Rearrange the first law of thermodynamics to solve for \( \Delta U \)
From the equation \( Q = \Delta U + W \), we can rearrange it to find \( \Delta U \):

\[ \Delta U = Q - W \]

### Step 3: Substitute the known values into the equation
Now, substitute the values of \( Q \) and \( W \) into the rearranged equation:

\[ \Delta U = 40 \, \text{joules} - 8 \, \text{joules} \]

### Step 4: Perform the calculation
Now, calculate \( \Delta U \):

\[ \Delta U = 40 - 8 = 32 \, \text{joules} \]

### Conclusion
The increase in internal energy of the system is \( \Delta U = 32 \) joules.

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