The first law of thermodynamics for a closed system is dU = dq + dw, where dw = `dw_(pv)+dw_("non-pv")`. The most common type of `w_("non-pv")` is electrical work. As per IUPAC convention work done on the system is positive.
A system generates 50 J of electrical energy and delivers 150 J of pressure-volume work against the surroundings while releasing 300 J of heat energy. What is the change in the internal energy of the system?

Options

A. `-100`
B. `-400`
C. `-300`
D. `-500`

Explanation

To solve the problem using the first law of thermodynamics, we need to analyze the given information step by step.

### Step 1: Understand the first law of thermodynamics
The first law of thermodynamics states that the change in internal energy (dU) of a closed system is equal to the heat added to the system (dq) plus the work done on the system (dw):
\[ dU = dq + dw \]

### Step 2: Identify the values given in the problem
- Electrical energy generated by the system: **50 J** (this is work done by the system, so it will be treated as negative when calculating dU)
- Pressure-volume work done by the system: **150 J** (this is also work done by the system, so it will be treated as negative)
- Heat released by the system: **300 J** (since heat is released, it will be treated as negative)

### Step 3: Assign the values to dq and dw
- Since the system releases heat, we have:
\[ dq = -300 \, \text{J} \]
- The total work done (dw) is the sum of pressure-volume work and electrical work:
\[ dw = -150 \, \text{J} \, (\text{pressure-volume work}) - 50 \, \text{J} \, (\text{electrical work}) \]
\[ dw = -150 - 50 = -200 \, \text{J} \]

### Step 4: Substitute dq and dw into the first law equation
Now, substitute the values of dq and dw into the first law equation:
\[ dU = dq + dw \]
\[ dU = (-300 \, \text{J}) + (-200 \, \text{J}) \]

### Step 5: Calculate the change in internal energy
Now, perform the calculation:
\[ dU = -300 - 200 = -500 \, \text{J} \]

### Final Answer
The change in the internal energy of the system is:
\[ \boxed{-500 \, \text{J}} \]

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