An ideal gas is filled in a closed rigid and thermally insulated container. A coil of `100Omega` resistor carrying current 1 A for 5 minutes supplies heat to the gas. The change in internal energy of the gas is

Options

A. `10 kJ`
B. `30 kJ`
C. `20 kJ`
D. `0 kJ`

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the given values
- Resistance of the coil (R) = 100 Ω
- Current (I) = 1 A
- Time (t) = 5 minutes = 5 × 60 seconds = 300 seconds

### Step 2: Calculate the heat generated by the resistor
The heat (H) generated by the resistor can be calculated using the formula:
\[ H = I^2 R t \]
Substituting the values:
\[ H = (1 \, \text{A})^2 \times (100 \, \Omega) \times (300 \, \text{s}) \]

### Step 3: Perform the calculation
Calculating the heat:
\[ H = 1 \times 100 \times 300 \]
\[ H = 30000 \, \text{J} \]

### Step 4: Relate heat to change in internal energy
Since the container is rigid and thermally insulated, the change in internal energy (ΔU) of the gas is equal to the heat generated:
\[ \Delta U = H \]
Thus,
\[ \Delta U = 30000 \, \text{J} \]

### Step 5: Convert to kilojoules
To express the change in internal energy in kilojoules:
\[ \Delta U = 30000 \, \text{J} = 30 \, \text{kJ} \]

### Final Answer
The change in internal energy of the gas is:
\[ \Delta U = 30 \, \text{kJ} \]

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