Test: Heat Engines - JEE MCQ

In a heat engine the ratio of net work done per cycle by the engine to the total amount of heat absorbed per cycle by the working substance from the source is known as Thermal Efficiency.

Dichlorodifluoromethane (R-12) is a colorless gas usually sold under the brand name Freon-12, and a chlorofluorocarbon halomethane (CFC) used as a refrigerant and aerosol spray propellant. Complying with the Montreal Protocol, its manufacture was banned in developed countries (non-article 5 countries) in 1996, and developing countries (article 5 countries) in 2010 due to concerns about its damaging impact to the ozone layer.[better source needed] Its only allowed usage is as fire retardant in submarines and aircraft. It is soluble in many organic solvents. Dichlorodifluoromethane was one of the original propellants for Silly String. R-12 cylinders are colored white.

Heat extracted from source Q1= 700 cal
Heat rejected to the sink Q2= 500 cal
Temperature of source T1= 150 +273= 423K
Temperature of sink T2 to be found:
 Q2/Q1 = T2/T1
So,
T2 = (Q2/Q1) x T1
= (500 x 423)/700
= 302.02 K
= 29.02 degree C.
 

According to Carnot theorem no heat engine working between two given temperatures of source and sink can be more efficient than a perfectly reversible engine working between the same two temperatures, by the statement of Carnot theorem.

4 is isobaric process, 1 is isochoric. Out of 3 and 2, 3 has the smaller slope (magnitude) hence is isothermal. Remaining process 2 is adiabatic.

Energy in 1 revolution=2 x P x a x l=2 x 9 x104 x 0.2 x0.6 j=21600J
Energy in n revolutions= 21600nJ
Power=E/t=21600n/t=21600 x 5=18000 J/s= 108000/746 h.p=144.77 h.p.

The ratio of quantity of heat removed per cycle from the contents of the refrigerator to the energy spent per cycle to remove this heat is called the coefficient of performance. It is the definition of coefficient of performance.

for hot reservoir I.e. source
temperature T₁=400k
heat supplied Q₁=800J
For cold reservoir i.e. sink
Temperature T₂=?
Heat supplied Q₂=640J
According to carnot’s theorem,
Q₁/Q₂= T₂/T₁
640/800= T₂/400
T₂=320k

Coefficient of performance(cop) of a refrigerator,
β= Q₂/Q₁-Q₂=T₂/T₁-T₂=277/300-277=277/23≈12
OR, Q₂/W=12. Therefore, W=1J.Q₂=12J
Also, Q1=Q2+W
=(12+1) J
=13J