A fan drawing electricity at a rate of 1.5 kW is located within a rigid enclosur

Question

A fan drawing electricity at a rate of 1.5 kW is located within a rigid enclosure, measuring 3m x 4m x 5m. The enclosure is filled with air, initially at 27 degrees C, 0.1 MPa. the fan operates steadily for 30 minutes. Assuming ideal gas behavior, determine for the air
a. The mass, in kg
b. The final temperature after 30 minutes, in degrees C. Do this calculation via two methods and compare them: i) assuming a constant specific heat at 300 K and ii) using the ideal gas air tables
c. The final pressure, in MPa
There is no heat transfer between the enclosure and the surroundings. Ignore the volume occupied by the fan itself and assume the fan stores no energy.

Explanation / Answer

state 1
volume = 3*4*5 = 60 m3

27 degrees = 300 k

0.1 MPA

a ) using the ideal gas equaion :

PV=mRT

where R , from tables , is : 0.287 , and the rest is known

(100)(60)=m(0.287)(300)

m= 69.7 kg

b) first law of thermodynamics :

Q+W = m(U + KE+PE )

W = m(U )       ( since there is no heat transfer , and KE and PE are negligable )

1.5*30*60 = 69.7 ( Cv ) ( T2- T1 )

1.5*30*60 = 69.7 ( 0.717 ) ( T2- 300)

T2 = 354 K =81 Degrees celcius

ii ) I found it from tables to be equal to 355 K

c ) again , ideal gas equaion

PV = mRT

where V does not change, m is constant and R = 0.287

assuming that the found temperature is correct :

P(60)=(69.7)(0.287)(354)

P = 118.03 Kpa

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