Question

Air is contained in a rigid well-insulated tank with a volume of 0.6 m3. The tank is fitted with a paddle wheel that transfers energy to the air at a constant rate of 4 W for 1 h. The initial density of the air is 1.2 kg/m3.

If no changes in kinetic or potential energy occur, determine:

(a) the specific volume at the final state, in m^3/kg
(b) the energy transfer by work, in kJ.
(c) the change in specific internal energy of the air, in kJ/kg.

Answer 1

Answers:

0.833 m³/kg

-14.4 kJ

20 kJ/kg

Answer 2

0.833 m³/kg

-14.4 kJ

20 kJ/kg

Step-by-step explanation:

`\rho` = Density = 1.2 kg/m³

`V` = Volume = 0.6 m³

t = Time taken = 1 hour

P = Power = 4 W

Mass is given by

`m=\rho V\\\Rightarrow m=1.2* 0.6\\\Rightarrow m=0.72\ kg`

As there is no change in kinetic and potential energy, the specific volume of the tank will be unaffected

`V_(s)=(0.6)/(0.72)\\\Rightarrow V_s=0.833\ m^3/kg`

The specific volume at the final state is 0.833 m³/kg

Energy is given by

`E=Pt\\\Rightarrow E=-4* 1* 3600\\\Rightarrow E=-14400\ J`

The energy transfer by work is -14.4 kJ

Change in specific internal energy is given by

`E=-m\Delta u\\\Rightarrow \Delta u=-(E)/(m)\\\Rightarrow \Delta u=-(-14.4)/(0.72)\\\Rightarrow \Delta u=20\ kJ/kg`

The change in specific internal energy is 20 kJ/kg