SOLVED PROBLEMS.

RITIK BHOLA

Retain in memory.

  • Efficiency of a reversible carnot engine(η) = w/q₂ = q₂-q₁/q₂=T₂-T₁/T₂
  • where,
  • w= Net work done by the system ( Joules /calories) ;
  • q₂= Heat absorbed by the system (Joules / calories) ;
  • q₁= Heat given to the sink (Joules / calories) ;
  • T₂= Temperature o fthe source (Kelvin) ;
  • T₁ = Temperature of the sink (kelvin) ;

EXAMPLE 1. Calculate the efficiency of a reversible carnot engine working between 100K and 500K. calculate the work obtainable in joules if the engine absorbs 1KJ of heat at the higher temperature.

Solution. Given : T₁ = 100K ; T₂ = 500K

Efficiency (η) = T₂-T₁/T₂

= 500-100/500

= 0.80

= 80%

EXAMPLE 2. Calculate the amount of heat supplied to carnot cycle working between 368K and 288K if the maximum work is obtained is 895 joule.

Solution. Given : T₂ = 368K ; T₁ = 288K ; w = 895 joule

now,                          w/q₂ = T₂-T₁/T₂

895/q₂ = 368 – 288 / 368

= 80/368

q₂ = 895 x 368 / 80

= 4117 joules

EXAMPLE 3. What should be the temperature of the sink for efficiency of carnot’s engine to be unity?

Solution.    Efiiciency of the carnot engine (η).

η = T2-T1/T2

since,                               η = 1

1 = T₂-T₁/T₂ 

or, T₂ – T₁ = T₂

or T₁ = 0K

= – 273ᵒ C

EXAMPLE 4. What percent T1 is of T2 for a heat engine whose efficiency is 50%?

Solution.  As we know that,

η= T₂-T₁/T₂

η = 50% = 0.5  (given)

T₂-T₁/T₂ = 0.5

or,

T₂-T₁ = 0.5 T₂

or,

T₁ is 50% of T₂

EXAMPLE 5. An engine operates between 1000K and 500K but passes the waste heat to the secon dengine which is working between 500K and 200K. What is the total efficiency obtained in this case?

Solution. Efficiency of the first engine.

η₁= 1000 – 500 / 1000

= 0.50

= 50 %

i.e. , 50% of heat is rejected to the second engine.

Efficiency of the second engine.

η₂ = 500 – 200 / 500

= 0.60

= 60%

i.e. , 60% of the rejected heat from first engine i.e. , 60% of 50% i.e. ,30% is converted into work .

∴         Total efficiency = 50% + 30% = 80%

LEARNING FACT

“AROUND 1% OF THE SUN’S MASS IS OXYGEN“

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