Question

Air is contained in a rigid well insulated tank with a volume of 0.2m^3 the tank is fitted with a paddle wheel which transfer energy to the air at a constant rate of 4 w for 20 min the initial density of the air is 1.2 kg/m^3 . If no change in K.E or P.E occur. Determine (a) the specific volume at the final state.(b) the change in specific internal energy of the air

Answer 1

Explanation:

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Answer 2

Answer: The specific volume at the final state is 0.833 m³ and the change in specific internal energy of the air is 20kJ/kg

Explanation:

(a) The specific volume will remain constant as the potential and kinetic energy remains constant.

Initial conditions :

Volume of air =  0.2 m³

Density of air = 1.2 kg/m³

Therefore,

⇒ Mass of air = Density × Volume

⇒ Mass of air =  1.2 × 0.2 kg = 0.24 kg

Specific volume = $\frac{Volume}{Mass}$

Specific volume of air  =   $\frac{0.2}{0.24}$ m³  =  0.833 m³

Final specific volume = Initial specific volume  

Final specific volume = 0.833 m³

(b) Rate of energy transfer to tank = 4 W

    Time = 20 min = 20 × 60 sec =  1200 sec

    Energy transferred to tank  = 4   × 1200 Joules = 4800 Joules

This energy gets stored in form of internal energy of air.

Change in internal energy ⇒ ΔU = 4800 J

Change in specific internal energy =  ΔU /Mass

Change in specific internal energy =  4800/0.24 J/kg

Change in specific internal energy =  20000 J/kg = 20kJ/kg

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