At steady state, a cycle develops a power output of 10 kW for heat addition at a rate of 10 kJ per cycle of operation from a source at 1500 K. Energy is rejected by heat transfer to cooling water at 300 K. Determine the minimum theoretical number of cycles required per minute.

Number of cycle per minute = 75

Explanation:

given data

Power output Wnet = 10 KW

Temperature of hot reservoir = 1500 K

Temperature of cold reservoir = 300 K

solution

we know that Efficiency is express as

n = 1 - To ÷ Tk     1

here  Tk is Temperature of hot reservoir and To is Temperature of cold reservoir

so put here value in equation 1 we get

n = 1- 300  ÷ 1500

n = 0.8

and Rate of heat input will be

Rate of heat input Qin = 10 × No. of cycles per sec

Rate of heat input Qin  = 10 n

and

n = Wnet ÷ 10 n    2

put here value

0.8 = 10 ÷  10 n

solve it we get

n = 1.25

so here Number of cycle per second is = 1.25

and Number of cycle per minute will be = 1.25 × 60

Number of cycle per minute = 75