Air enters a compressor operating at steady state with pressure of 90 kPa, at a temperature of 350 K, and a volumetric flow rate of 0.6 m3/s. The air exits the compressor at a pressure of 700 kPa. Heat transfer from the compressor to its surrounding occurs at a rate of 30 kJ/kg of air flowing. The compressor power input is 75 kW. Neglecting kinetic and potential energy effects and assuming air to be an ideal gas, find the exit temperature of air.

Explanation:

Before determining the exit temperature of air, it is required to find the specific enthalpy at outlet by using the First Law of Thermodynamics:

An ideal gas observes the following mathematical model:

Where:

- Absolute pressure, in kilopascals.

- Volume, in cubic meters.

- Quantity of moles, in kilomole.

- Ideal gas universal constant, in .

- Absolute temperature, in kelvin.

The previous equation is re-arranged in order to calculate specific volume at inlet:

The mass flow is:

The specific enthalpy in ideal gases depends on temperature exclusively. Then:

The specific enthalpy at outlet is:

The exit temperature of air is:

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