200 joules of heat was supplied to a system at constant volume. It resulted in the increase in temperature of the system from 298 to 323 K. What is the change in internal energy of the system ?

Options

A. 400 J
B. 200 J
C. 50 J
D. 150 J

Explanation

To find the change in internal energy of the system, we can follow these steps:

### Step 1: Understand the First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W):
\[ \Delta U = Q + W \]

### Step 2: Identify the Conditions of the Problem
In this problem, we are given that the heat supplied to the system is 200 joules and that the process occurs at constant volume. At constant volume, the work done (W) is zero:
\[ W = 0 \]

### Step 3: Substitute Values into the First Law Equation
Since the work done is zero, the equation simplifies to:
\[ \Delta U = Q \]
Given that 200 joules of heat was supplied to the system, we can substitute this value into the equation:
\[ \Delta U = +200 \, \text{J} \]

### Step 4: Conclusion
Thus, the change in internal energy of the system is:
\[ \Delta U = 200 \, \text{J} \]

### Final Answer
The change in internal energy of the system is **200 joules**.

---