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 pass 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`
The final temperature of nitrogen is

Options

A. `2.6^(@) C`
B. `56.6^(@)C`
C. `29.6^(@) C`
D. `5.67 ^(@)C`

Answer

B

Explanation

Heat loss, `Q_(1)=2800J`
Work done at constant pressure `= n C_(p) Delta T`
`( :' C_(p)=(7R)/(2)=(7)/(2)xx(25)/(3)=(175)/(6) kJ //mol-K)`
`Q-W_(C)=nC_(p)DeltaT`
`-2.8kJ-(-72kJ)=(0.08xx175)/(6)DeltaT`
`implies DeltaT=((69.2kJ))/((0.08 k mol)((175)/(6)-kJ//kmol-K))`
`=29.6 K`
Final temperature `=27+29.6`
`=56.6^(@)C`