Question

Two kilograms of air is contained in a rigid wellinsulated tank with a volume of 0.6 m3 . The tank is fitted with a paddle wheel (stirrer) that transfers energy to the air at a constant rate of 10 W for 1h. If no changes in kinetic or potential energy occur, determine a) The specific volume at the final state, in m3 /kg. b) The energy transfer by work, in kJ. c) The change in specific internal energy of the air, in kJ/kg.

Answer 1

`0.3\ \text{m}^3/\text{kg}`

`36\ \text{kJ}`

`18\ \text{kJ/kg}`

Step-by-step explanation:

V = Volume of air =
`0.6\ \text{m}^3`

P = Power = 10 W

t = Time = 1 hour

m = Mass of air = 2 kg

Specific volume is given by

`v=(V)/(m)\\\Rightarrow v=(0.6)/(2)\\\Rightarrow v=0.3\ \text{m}^3/\text{kg}`

The specific volume at the final state is
`0.3\ \text{m}^3/\text{kg}`

Work done is given by

`W=Pt\\\Rightarrow W=10* 60* 60\\\Rightarrow W=36000\ \text{J}=36\ \text{kJ}`

The energy transfer by work, is
`36\ \text{kJ}`

Change in specific internal energy is given by

`\Delta u=(Q)/(m)+(W)/(m)\\\Rightarrow \Delta u=0+(36)/(2)\\\Rightarrow \Delta u=18\ \text{kJ/kg}`

The change in specific internal energy of the air is
`18\ \text{kJ/kg}`