Final answer:
The rate of heat transfer to the cooling water circulating through the water jacket is 150 kW.
Step-by-step explanation:
To determine the rate of heat transfer to the cooling water circulating through the water jacket, we can use the first law of thermodynamics, which states that the heat transfer is equal to the change in internal energy plus the work done. Since the compressor is operating at steady state, the change in internal energy is zero.
Therefore, the rate of heat transfer can be calculated as:
Rate of heat transfer = Compressor power - Rate of work done = 150 kW - 0 = 150 kW
Therefore, the rate of heat transfer to the cooling water is 150 kW.