Answer:
The rate of heat gain of the exercise room = 20.87kW
Explanation:
Given
Weight-lifting machines = 6
Number of treadmills = 7
Number of people doing exercise = 13 + 2 = 15
Heat Dissipation = 600W
Motor Load Factor = 0.7
Motor Efficiency = 0.77
Motor Power Output = 2.5hp
First, we calculate the motor total shaft power output
This is calculated as follows
W = Number of treadmills * Motor Power Output
W = 7 * 2.5hp ---- Convert to Watt
W = 7 * 2.5 * 746W
W = 13,055W
Then we calculate the heat generated, Q from the motor.
This is calculated from efficiency formula:
Eff = W * Load Factor / Q --- Make Q the subject of formula
Q = W * Load Factor / Eff
Q = 13,055 *0.7 / 0.77
Q = 11868.18181818181
Q = 11868.18W
Then we Calculate the heat from people doing exercise
Q2 = number of people * heat dissipation
Q2 = 15 * 600
Q2 = 9000W
Total heat gain is then calculated as:
9000W + 11868.18W
= 20,868.18W or 20.87kW
The rate of heat gain of the exercise room = 20.87kW