Final answer:
The power input to the industrial refrigeration system's compressor, using the simplified steady-state no-change internal energy assumption and given the heat transfer is 6 kW.
Step-by-step explanation:
To calculate the power input to the compressor in the industrial refrigeration system using ammonia as the working fluid, we need to apply the first law of thermodynamics for steady-state systems. The refrigeration system operates under steady-state conditions and kinetic and potential energy effects are negligible; hence, we can simplify the energy equation to:
Ü = −Q − W where Ü is the change in internal energy (which is zero for steady-state), Q is the heat transfer, and W is the work done by the system.
Given:
Heat transfer from the compressor, Q = 6 kW (negative since it is an output)
Thus, the work done by the compressor is:
W = -(Ü + Q)
Since the change in internal energy, Ü, is zero, we get:
W = -Q = -(-6 kW) = 6 kW
However, this is the heat transfer from the compressor. The power input to the compressor is the work that needs to be supplied to the system. Assuming the compressor is not 100% efficient and does not include other losses, the actual power input might be different. In this case, additional information, such as the efficiency of the compressor, would be required to determine the real power input.
If the compressor operation is considered to be isentropic (no entropy generation, which implies a reversible and adiabatic process), then the heat transfer would be zero, and all the power input to the compressor would be translated into work done on the refrigerant. Therefore, without further efficiency or loss of information, we can assume the work done on the refrigerant is the same as the power input, which is 6 kW.