High School

170 students sit in an auditorium listening to a physics lecture. Each is using 125 W of metabolic power. An air conditioner with a COP of 5.0 is used to maintain a constant room temperature.

What minimum electric power must be used to operate the air conditioner?

Answer :

The calculated power is P = 3500 W. Power can be defined as the amount of work completed in a given amount of time.

Watt (W), which is derived from joules per second (J/s), is the SI unit of power. Horsepower (hp), which is roughly equivalent to 745.7 watts, is a unit of measurement sometimes used to describe the power of motor vehicles and other devices.

There are n = 140 students in the auditorium overall.

Each pupil is using a metabolic power of p = 125 W.

To keep the temperature in the auditorium consistent, the air conditioner's coefficient of performance (COP) is listed as 5.

Let P represent the required minimum amount of electric power to operate the air conditioner.The fact that

np = P in COP

P = np/COP

= ( 140 x 125 ) / 5

= 3500 W

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