Question

Air enters a compressor at 14.7 psia and 77∘F and is compressed to 140 psia and 80∘F. Determine the minimum work required for this compression, in Btu/lbm, with the same inlet and outlet states. Does the minimum work require an adiabatic compressor?

Answer 1

To determine the minimum work required for this compression, we can use the first law of thermodynamics and the adiabatic compression formula. The specific heat capacity at constant volume and the changes in temperature need to be calculated to find the work done.

Step-by-step explanation:

To determine the minimum work required for this compression, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat transferred to the system minus the work done by the system.

In this case, the compression is adiabatic, which means that no heat is transferred to or from the system. Therefore, the change in internal energy is equal to the work done by the system.

The work done by an adiabatic compression can be calculated using the formula:

W = Cv * (T2 - T1)

Where W is the work done, Cv is the specific heat capacity at constant volume, and T2 and T1 are the final and initial temperatures, respectively.

Given the temperatures and pressures provided in the question, we can calculate the specific volume at each state using the ideal gas law. Then, we can use the specific volumes to determine the change in temperature and calculate the work done.

Answer 2

The minimum work required for compressing the air can be calculated using the equation W = Cv(T2 - T1) - R ln (P2/P1). Since the compression is adiabatic, there is no heat transfer, and the minimum work done would not require an adiabatic compressor.

Step-by-step explanation:

The minimum work required for compressing the air can be calculated using the equation:

W = Cv (T2 - T1) - R ln (P2/P1)

Where:

• W is the work done in Btu/LBM
• Cv is the specific heat constant volume of air
• T2 and T1 are the final and initial temperatures
• R is the gas constant
• P2 and P1 are the final and initial pressures

Since the compression is adiabatic, there is no heat transfer, and the minimum work done would not require an adiabatic compressor.