Examples of Unsteady-State Applications

Example 1

An insulated rigid tank of volume 0.3m³ is connected to a large pipeline carrying air at 1400 kPa and 300°C. The valve between the pipeline and the tank is opened and the tank fills with air until the pressure is 1400 kPa and then the valve is closed. Determine the final temperature of the air in the tank if:

a) The tank is initially empty,
b) The tank initially contains air at 350 kPa and 139°C.

Solution

Assume the system is the contents of the tank. 

Example 2

A rectangular steel tank having an internal volume of 1m³ contains air at 2.5MPa and 20°C. A relief valve is opened slightly allowing air to escape to the atmosphere. The valve is closed when the pressure in the tank reaches 350 kPa:

a) Calculate the amount of heat that must be added so as to keep the tank contents at 20°C throughout the process.

b) Calculate the final temperature if the process takes place adiabatically.

Solution

Note:

The result of equation 14 informs us that the gas that remains in the tank undergoes a reversible adiabatic expansion. Hence, the problem can be solved by choosing the contents of the tank in the final state as the system. The same amount of gas occupies less volume at the initial state as shown:

This is a closed system and since the gas on one side of the imaginary boundary has the same temperature as the gas on the other side we can assume the system is adiabatic as no heat is exchanged across the boundary. 

Furthermore, with the exception of the region around the valve - which is outside our chosen system - the gas in the cylinder is undergoing a uniform expansion thus there is no pressure, velocity or temperature gradients within the cylinder. Thus it can be assumed that the changes occurring in the system are reversible.