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`
Number of moles of nitrogen gas is

Options

A. `0.8 k mol`
B. `0.08 k mol`
C. `0.8 mol`
D. `0.08 mol`

Explanation

To find the number of moles of nitrogen gas in the piston-cylinder device, we can use the ideal gas equation, which is given by:

\[ PV = nRT \]

Where:
- \( P \) = Pressure (in Pa)
- \( V \) = Volume (in m³)
- \( n \) = Number of moles
- \( R \) = Ideal gas constant (in J/(kmol·K))
- \( T \) = Temperature (in K)

### Step 1: Convert the given values to appropriate units
- Pressure \( P = 400 \, \text{kPa} = 400 \times 10^3 \, \text{Pa} \)
- Volume \( V = 0.5 \, \text{m}^3 \)
- Temperature \( T = 27^\circ C = 27 + 273 = 300 \, \text{K} \)
- The value of \( R = \frac{25}{3} \, \text{kJ/(kmol·K)} = \frac{25 \times 10^3}{3} \, \text{J/(kmol·K)} \)

### Step 2: Substitute the values into the ideal gas equation
We can rearrange the ideal gas equation to solve for \( n \):

\[ n = \frac{PV}{RT} \]

Substituting the values we have:

\[ n = \frac{(400 \times 10^3 \, \text{Pa}) \times (0.5 \, \text{m}^3)}{\left(\frac{25 \times 10^3}{3} \, \text{J/(kmol·K)}\right) \times (300 \, \text{K})} \]

### Step 3: Calculate the numerator
Calculating the numerator:

\[ 400 \times 10^3 \times 0.5 = 200000 \, \text{Pa·m}^3 = 200000 \, \text{J} \]

### Step 4: Calculate the denominator
Calculating the denominator:

\[ R \times T = \left(\frac{25 \times 10^3}{3}\right) \times 300 = \frac{25 \times 300 \times 10^3}{3} = \frac{7500 \times 10^3}{3} = 2500 \times 10^3 \, \text{J/kmol} \]

### Step 5: Calculate the number of moles
Now substituting back into the equation for \( n \):

\[ n = \frac{200000}{2500 \times 10^3} \]

### Step 6: Simplify the fraction
\[ n = \frac{200000}{2500000} = \frac{2}{25} \]

### Step 7: Convert to kilo moles
To convert to kilo moles:

\[ n = \frac{2}{25} \, \text{kmol} = 0.08 \, \text{kmol} \]

### Final Answer
Thus, the number of moles of nitrogen gas is:

\[ n = 0.08 \, \text{kmol} \]