Carnot Engine - Practice Questions & MCQ

• Carnot Engine-

          As shown in the below figure, It consists of the following parts

        

      1.A cylinder with perfectly non-conducting walls and a perfectly conducting base containing an ideal gas as working
         substance and fitted with a non-conducting frictionless piston.

      2. A source of infinite thermal capacity maintained at a constant higher temperature T₁

     3. A sink of infinite thermal capacity maintained at a constant lower temperature T₂

      4. A perfectly non-conducting stand for the cylinder.

• Carnot cycle-

  As shown in the below figure, It consists of the following 4 processes.

 

1. Isothermal expansion (curve AB)

The cylinder containing ideal gas as working substance allowed to expand slowly at this constant temperature T₁

So Work done = Heat absorbed by the system

2. Adiabatic expansion (curve BC)

The cylinder is then placed on the non-conducting stand and the gas is allowed to expand adiabatically till the
temperature falls from T₁ to T₂

 

3. Isothermal compression (curve CD)

The cylinder is placed on the sink and the gas is compressed at constant temperature T₂.
Work done = Heat released by the system

4. Adiabatic compression (curve DA)

Finally, the cylinder is again placed on a non-conducting stand and the compression is continued so that gas returns to its initial stage.

• The efficiency of the Carnot cycle ()

The efficiency of the engine is defined as the ratio of work done to the heat supplied.

Net work done during the complete cycle

Putting the values we get

 ..... (1)

Since points, B and C lie on the same adiabatic curve 

......(2)

Also, point D and A lie on the same adiabatic curve

....(3)

From the equation (2) and (3) we get

 .....(4) 

Put equation (4)  in equation (1) we get 

The efficiency of the Carnot engine as

      So 

      where 

             Source temperature  ,  Sink Temperature   and    

           and      are in kelvin

   From the above formula, we can conclude that

      1. The efficiency of a heat engine depends only on temperatures of source and sink and is independent of all other factors.

      2. As a Carnot engine is the ideal engine, So no heat engine can be more efficient than Carnot engine.

      3. All reversible heat engines working between same temperatures are equally efficient   

     4. Since    So the efficiency of a Carnot engine is always lesser than unity.

• Carnot Theorem (The relation between Heat and Temperature in the Carnot cycle)

           i.e     

              where 

 Heat absorbed

 Heat released

 Low temperature

 Higher Temperature