Answer to Question #206660 in Molecular Physics | Thermodynamics for Yomna

Question

 A rigid tank of 2 m3

volume contains pressurized air at 400 kPa and 25∘

C. The tank slowly deflates through a small hole in the tank wall. Due to 

the loss of air, the pressure drops to 100kPa and due to heat transfer with 

the environment, the temperature of the air in the tank remains on 25∘C. 

Calculate the net heat transfer.

Answer 1

$V=const,$

$\frac{p_1}{T_1}=\frac{p_2}{T_2},\implies T_2=74.5~K,$

$\Delta U=\frac 32 \nu R\Delta T=\frac 32 \frac{p_1 V}{RT_1}R\Delta T=\frac{3p_1V\Delta T}{2T_1}=\frac{3\cdot 400000\cdot 2\cdot (298-74.5)}{2\cdot 298}=0.9~MJ.$