Consider a well-insulated 20-L evacuated rigid tank that is surrounded by atmosp

Question

Consider a well-insulated 20-L evacuated rigid tank that is surrounded by atmospheric air (Treat the air as an ideal gas with R = 0.287 kJ/kg*K, Cp = 0.1.005 kJ/kg*K, Cv = 0.718 kJ/kg*K, and k = 1.4) at P atm = 100 kPa, T atm = 27 degree C. A valve at the neck of the bottle is opened and the atmospheric air is allowed to flow into the bottle until mechanical equilibrium with the surroundings (P tank = P^) has been attained. What is the temperature and mass of the air in the tank after the adiabatic process? T2 (K): 420 m2(kg): 0.0166

Explanation / Answer

Let p1v1T1 are pressure , vol and temp. of the air in atm.

from ideal gas equation (air is ideal gas)

P1V1 = RT1

100* V1 = 1 * .287 * (27+373),

V1 = specific vol( at m=1kg) = .861 m^3/ kg

P1=P2

P1V1 /T1 = P2V2 / T2

0.861 / 300 = 20* 10^-3 / T2 ( vol = 20 lit = V2)

T2 = 6.96 K  

P2V2 = mRT2

100* 20 * 10^-3 = m *.287 * 6.96

m2 = 1 kg

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