Question

2. a A nuclear power plant operates at 65 percent of its maximum theoretical (Carnot) efficiency between temperatures of 520^oC and 270°C. If the plant produces electric energy at the rate of 1.55 Giga-Watts, how much exhaust heat is discharged per hour?
Joules

b. A cord of mass 0.44 kg is stretched between two supports 28.0 m apart. If the tension in the cord is 145 N, how long will it take a pulse to travel from one support to the other?
seconds

Answer 1

Carnot efficiency is the maximum efficiency we can get when a heat engine is working between two different temperatures.

Given that

Carnot efficiency between between temperatures of 520 ^o C and 270°C is 65%

The rate at which electric energy is produced is 1.55 G W

equation of Carnot efficiency

here

= 793.15 K

=543.15 K

put values we get

E_C = 0.31

the Carnot efficiency of the plant is 0.31

Given that the plant works 65 % of its efficiency

then efficiency = 0.31*0.65 =0.20

efficiency is 0.20

and we know efficiency is the ratio of total power to the usable power generated.

so

here

Total power is 7.75 G W.

so here we can see

6.2 GW power is wasted here. this will go as exhaust heat.

energy=power*time

(1 GW is 10⁹ Watts )

223.2*10¹¹ J

exhaust heat is discharged per hour will be 2.23*10¹³ J