Question

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.

Answer 1

Number of cycle per minute = 75

Step-by-step 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