CHEMICAL ENGINEERING

Please provide a detailed solution, given that I am a beginner in the subject

The motor of a system, which generates thermal energy at a constant rate of 8.99 MJ/min, is cooled by air entering and leaving the equipment. The air inside the system circulates fast enough for its temperature to be considered uniform and equal to the temperature of the exhaust air. Air passes through the body of the equipment at a speed of 2.72 kmol/min, and enters at a temperature of 18.33 C; The system contains 90.72 moles of air inside. The equipment releases heat to the surroundings at a rate:

Q(KJ/min) = -1148 + 62.62T, where Q has units KJ/min and T has units C

For calculation purposes, consider the Cp of the air constant and equal to 29.15 kJ/(kmolK). Considering that the system turns on when the air temperature inside is equal to 18.33C:

a) Calculate the air temperature in the steady state, if the system operates continuously for an indefinite period of time. (Solution: 81.7 C).

b) Find a differential equation for the variation of the exhaust air temperature with time, since the start-up, and solve it. (Solution T = 81.7 - 63.4e^(-75.08t))