A tank contains CO2 gas at 25oC and 500 kPa. A valve on the tank is opened slightly so that the CO2 slowly exits the tank until the pressure inside the tank drops to 100 kPa. The volume of the tank is 0.25 m3. Determine the amount of heat transfer necessary so that the CO2 in the tank remains at 25oC throughout the process.

Question

State e: Outlet; State 1: Initial State; State 2: Final State
Given: CO2; Te = 25oC; V = 0.25 m3; P1 = 500 kPa; P2 = 100 kPa; T1 = T2 = 25oC
Assume: As no information is given and these terms are unlikely to be significant, W = 0, and kinetic and potential energy can be neglected. No flow into the tank (mi = 0). CO2 is an ideal gas with variable specific heats.

Answer 1

Solution: With the assumptions given employed, the general First Law can be reduced to
Q - mehe = m2u2 - m1u1
At T = 25oC, he = 205.93 kJ/kg; u1 = u2 = 156.44 kJ/kg
From the ideal gas law, m1 = P1V/RT1 = = 2.221 kg
m2 = P2V2 / RT2 = 0.4441 kg
where R = 0.1889 kJ/kg-K, and T = 298 K for each state.
From the conservation of mass: me = m1 – m2 =1.78 kg
Solving for the heat transfer yields Q = 88.1 kJ .
The temperature of the CO2 will naturally decrease as the pressure in the tank drops, and so heat must be added to maintain a constant temperature.