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A reversible engine has efficiency of 1/4. If the temperature of the sink is reduced by 58° C, its efficiency becomes double. Calculate the temperature of the sink.
- a)280°C
- b)382°C
- c)174°C
- d)180.4°C
Correct answer is option 'C'. Can you explain this answer?
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A reversible engine has efficiency of 1/4. If the temperature of the s...
Given data:
Efficiency of the reversible engine, η = 1/4
Change in temperature of the sink, ∆T = 58°C
Let's solve the problem step by step:
1. Calculate the initial temperature of the sink:
Efficiency of a reversible engine is given by the formula:
η = 1 - (Tc/Th)
where Tc = temperature of the sink and Th = temperature of the source
Given efficiency, η = 1/4
1/4 = 1 - (Tc/Th)
Tc/Th = 3/4
Th = (4/3)Tc
2. Calculate the final temperature of the sink:
When the temperature of the sink is reduced by 58°C, the new efficiency becomes double the initial efficiency:
New efficiency = 2 * 1/4 = 1/2
Now, efficiency with reduced temperature:
1/2 = 1 - (Tc - 58)/Th
Substitute Th = (4/3)Tc from step 1:
1/2 = 1 - (Tc - 58)/(4/3)Tc
1/2 = 1 - 3(Tc - 58)/(4Tc)
3(Tc - 58)/(4Tc) = 1/2
6(Tc - 58) = 4Tc
6Tc - 348 = 4Tc
2Tc = 348
Tc = 174°C
Therefore, the temperature of the sink is 174°C, which corresponds to option C.
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A reversible engine has efficiency of 1/4. If the temperature of the sink is reduced by 58° C, its efficiency becomes double. Calculate the temperature of the sink.a)280°Cb)382°Cc)174°Cd)180.4°CCorrect answer is option 'C'. Can you explain this answer?
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