Final answer:
The exit temperature of air after compression can be calculated by applying the first law of thermodynamics, accounting for the heat transfer and work done during the process, with the specific heat capacity of air under constant pressure.
Step-by-step explanation:
The exit temperature of the air after it has been compressed in a compressor can be calculated by considering the first law of thermodynamics and the heat transfer during the process. The first law of thermodynamics, which is a manifestation of the conservation of energy, states that the change in internal energy of a system is equal to the net heat transfer into the system minus the net work done by the system. A heat pump is an example of a device that compresses air to raise its temperature and then allows for heat transfer to a room or space.
To calculate the final temperature, we need to know the initial conditions of the air, the work input (work input W), and the heat transfer rate. The heat required to raise the temperature of air can be expressed as Q = mcΔT, where m is the mass of the air, c is the specific heat capacity, and ΔT is the change in temperature. In assessing the heat transfer in the compressor, we must consider this equation along with the work done by the compressor.
Without the specific values for mass, specific heat capacity, initial and final pressures, and the work done, it is not possible to give a numerical answer. However, the concept to calculate exit temperature includes application of the first law of thermodynamics, the specifics of heat transfer and considerations of constant pressure specific heat of air in a heat engine cycle.