A system does `100J` work on surroundings by absorbing `150J` of heat. Calculate the change in internal energy.

Options

A. 100 J
B. 50 J
C. 25 J
D. 150 J

Explanation

To solve the problem, we will use the First Law of Thermodynamics, which states that the change in internal energy (ΔE) of a system is equal to the heat exchanged (q) plus the work done (W) on the system. The formula can be expressed as:

\[ \Delta E = q + W \]

### Step 1: Identify the heat absorbed by the system
The system absorbs 150 J of heat. According to the sign convention, when heat is absorbed by the system, it is considered positive. Thus, we have:

\[ q = +150 \, \text{J} \]

### Step 2: Identify the work done by the system
The system does 100 J of work on the surroundings. When work is done by the system, it is considered negative in the context of the First Law of Thermodynamics. Therefore, we have:

\[ W = -100 \, \text{J} \]

### Step 3: Substitute the values into the formula
Now, we can substitute the values of q and W into the equation for ΔE:

\[ \Delta E = q + W = 150 \, \text{J} + (-100 \, \text{J}) \]

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

\[ \Delta E = 150 \, \text{J} - 100 \, \text{J} = 50 \, \text{J} \]

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

\[ \Delta E = 50 \, \text{J} \]

### Final Answer
The change in internal energy is **50 J**.

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