A reversible Carnot engine converts 1/6th of heat into input works. When the temperature of the sink is reduced by 62˚C then the efficiency is doubled. The temperature of the source and sink is:
Correct answer: D. 99˚C, 37˚C
- A. 80˚C, 37˚C
- B. 99˚C, 30˚C
- C. 99˚C, 25˚C
- D. 99˚C, 37˚C
Explanation
The efficiency of the engine = η = Work / Qinput.As W = ⅙ QinputAlso η = 1 - T2/T1 T1 and T2 are the temperatures of source and sink.⅙ = 1 - T2/T1T1 = 1.2 T2 (1)Now the sink temperature is reduced by 62oC, T2' = T2 - 62Also the new efficiency η' = 2 × ⅙ = 2/6η' = 1 - T2' /T12/6 = 1 - T2 - 62 / 1.2 T2T2 = 310 KT2 = 310 - 273 = 37o CFrom (1)T1 = 1.2 × 310 = 372K T1 = 372 - 273 = 990 CThis is numerical so it can only have one answer so option D is correct.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Thermal Equilibrium and Heat
Thermal equilibrium means that bodies in contact have the same temperature and no net heat flows between them. The topic distinguishes heat from temperature, uses the zeroth law of thermodynamics, and covers heat transfer, specific heat capacity, thermal expansion and the conditions for reaching equilibrium.
Practise Thermodynamics
714 free Thermodynamics MCQs from Physics, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Physics questions like this
Physics is on 16 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Thermal Equilibrium and Heat questions
Which of the following is equivalent to a temperature -50oC?
100 W heater is switched on for 5 minutes to melt ice. What is the mass of ice that melts at 0oC? ( The specific latent heat of fusion of ice is 334 J/g).
100 W heater is used to melt 50 g of ice at OC. How long should the heater be switched on? (Specific latent heat of fusion of ice is 334 J/g)
A 1.0 kW heater supplies energy to a liquid of mass 1 kg. The temperature of the liquid changes by 80 K in a time of 400 s. The specific heat capacity of the liquid is 4.0 kJ / kg*K. What is the average power lost by the liquid?
A 300 W heater is used to boil 500g of water at l00 °C. How long should the heater be switched on? (The specific latent heat of vaporization of water is 2230 J/g).
How much energy is required to raise the temperature of 5.00 kg of lead from 20.0•c to its melting point of 327°C? The specific heat of lead is 128 J/kg ?•c.