Piston cylinder device initially contains `0.5m^(3)` of nitrogen gas at `400 kPa` and `27^(@)C`. An electric heater within the device is turned on and is allowed to apss a current of `2 A` for `5 mi n` from a `120 V` source. Nitrogen expands at constant pressure and a heat loss of `2800 J` occurs during the process.
`R=25//3 kJ //k mol - K`
Electric work done on the nitrogen gas is

Options

A. `72 kJ`
B. `36 kJ`
C. `118 kJ`
D. `9kJ`

Explanation

To solve the problem of calculating the electric work done on the nitrogen gas in the piston-cylinder device, we will follow these steps:

### Step 1: Calculate the Power
The power (P) supplied by the electric heater can be calculated using the formula:
\[ P = V \times I \]
Where:
- \( V = 120 \, \text{V} \) (voltage)
- \( I = 2 \, \text{A} \) (current)

Substituting the values:
\[ P = 120 \, \text{V} \times 2 \, \text{A} = 240 \, \text{W} \]

### Step 2: Convert Time to Seconds
The time (t) for which the current flows is given as 5 minutes. We need to convert this into seconds:
\[ t = 5 \, \text{minutes} \times 60 \, \text{seconds/minute} = 300 \, \text{seconds} \]

### Step 3: Calculate the Total Work Done
The work done (W) can be calculated using the formula:
\[ W = P \times t \]
Substituting the values:
\[ W = 240 \, \text{W} \times 300 \, \text{s} = 72000 \, \text{J} \]
Since \( 1 \, \text{kJ} = 1000 \, \text{J} \):
\[ W = 72 \, \text{kJ} \]

### Step 4: Determine the Sign of Work Done
In thermodynamics, work done on the system is considered negative. Therefore, the work done on the nitrogen gas is:
\[ W = -72 \, \text{kJ} \]

### Final Answer
The electric work done on the nitrogen gas is:
\[ \boxed{-72 \, \text{kJ}} \]

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