In a process, a system does 140 J of work on the surroundings and only 40 J of heat is added to the system, hence change in internal energy is

Options

A. 180 J
B. `-180` J
C. 100 J
D. `-100` J

Answer

To find the change in internal energy of the system, we can use the first law of thermodynamics, which is given by the equation:

\[ \Delta U = Q - W \]

Where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat added to the system,
- \(W\) is the work done by the system on the surroundings.

### Step 1: Identify the values
From the problem statement:
- Work done by the system on the surroundings, \(W = 140 \, \text{J}\) (this will be taken as negative in our calculation).
- Heat added to the system, \(Q = 40 \, \text{J}\).

### Step 2: Assign the correct signs
Since the system is doing work on the surroundings, we assign a negative sign to work:
\[ W = -140 \, \text{J} \]
The heat added to the system is positive:
\[ Q = +40 \, \text{J} \]

### Step 3: Substitute the values into the equation
Now we can substitute the values of \(Q\) and \(W\) into the first law of thermodynamics equation:
\[ \Delta U = Q - W \]
Substituting the values:
\[ \Delta U = 40 \, \text{J} - (-140 \, \text{J}) \]

### Step 4: Simplify the equation
This simplifies to:
\[ \Delta U = 40 \, \text{J} + 140 \, \text{J} \]
\[ \Delta U = 180 \, \text{J} \]

### Step 5: Calculate the change in internal energy
However, we need to remember that the work done by the system is negative:
\[ \Delta U = 40 \, \text{J} - 140 \, \text{J} \]
\[ \Delta U = -100 \, \text{J} \]

### Final Answer
Thus, the change in internal energy is:
\[ \Delta U = -100 \, \text{J} \]

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