An insulated piston-cylinder device contains 100 L of air at 400 kPa and 25°C. A paddle wheel within the cylinder is rotated until 15 kJ of work is done on the air while the pressure is held constant. Determine the final temperature of the air. Neglect the energy stored in the paddle wheel. (Page 172).

T'=70.92°C

Explanation:

Given that

V = 100 L=0.1 m³

P=400 KPa

T=25°C

Work done on the air = 15 KJ

W = - 15 KJ

If we assume that air is ideal gas

P V = m R T

R=0.287 KJ/kg. K for air

T = 273 + 25 = 298 K

By putting the values

P V = m R T

400 x 0.1 = m x 0.287 x 298

m=0.46 kg

From first law of thermodynamics

Q = ΔU + W

Insulated piston-cylinder, Q=0

ΔU = m Cv ΔT

ΔU = - W

Cv = 0.71 KJ/kg. k for air

0.46 x 0.71 x (T' - 25) = 15

T'=70.92 °C

So the final temperature of air is T'=70.92 °C