1 Engine 1 has an efficiency of 012 and requires 7100 J of i

1. Engine 1 has an efficiency of 0.12 and requires 7100 J of input heat to perform a certain amount of work. Engine 2 has an efficiency of 0.31 and performs the same amount of work. How much input heat does the second engine require?

2. An engine has a hot-reservoir temperature of 970 K and a cold-reservoir temperature of 640 K. The engine operates at three-fifths maximum efficiency. What is the efficiency of the engine?

3. A Carnot engine operates between temperatures of 760 and 341 K. Calculate what the efficiency would be if (a) the temperature of the hot reservoir were raised by 53.4 K or (b) if the temperature of the cold reservoir were lowered by 53.4 K. (Give a decimal number between zero and one in both cases.)

Solution

THe energy needed for the work

Heat supplied * efficiency = work

7100*0.12 = 852 J

Hence the heat need by engine 2

HEat= 852/0.31 = 2748 J

2 . The maximum efficiency of carnot engine is given by

e = Th -Tc/Th = 970-640/970 = 0.34

It is operating at = 3/5 max efficiency = 0.204