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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.

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boffeemadrid

Answer:

0.833 m³/kg

-14.4 kJ

20 kJ/kg

Explanation:

[tex]\rho[/tex] = Density = 1.2 kg/m³

[tex]V[/tex] = Volume = 0.6 m³

t = Time taken = 1 hour

P = Power = 4 W

Mass is given by

[tex]m=\rho V\\\Rightarrow m=1.2\times 0.6\\\Rightarrow m=0.72\ kg[/tex]

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

[tex]V_{s}=\dfrac{0.6}{0.72}\\\Rightarrow V_s=0.833\ m^3/kg[/tex]

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

Energy is given by

[tex]E=Pt\\\Rightarrow E=-4\times 1\times 3600\\\Rightarrow E=-14400\ J[/tex]

The energy transfer by work is -14.4 kJ

Change in specific internal energy is given by

[tex]E=-m\Delta u\\\Rightarrow \Delta u=-\dfrac{E}{m}\\\Rightarrow \Delta u=-\dfrac{-14.4}{0.72}\\\Rightarrow \Delta u=20\ kJ/kg[/tex]

The change in specific internal energy is 20 kJ/kg

Answers:

0.833 m³/kg

-14.4 kJ

20 kJ/kg

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