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Carnot engine takes one thousand kilo ca...

Carnot engine takes one thousand kilo calories of heat from a reseervoir at `827^@C` and exhausts it to a sink at `27^@C`. How, much work does it perform? What is the efficiency of the engine?

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
Given, `Q_1=10^6cal`
`T_1=(827+273)=1100K`
and `T_2=(27+273)=300K`
as, `Q_2/Q_1=T_2/T_1` (in Carnot engine)
`:.` `Q_2=T_2/T_1*Q_1=(300/1100)(10^6)`
`=2.72xx10^5cal`
Efficiency of the cycle,
`eta=(1-(T_2)/(T_1))xx100`
or `eta=(1-300/1100)xx100`
`72.72%`
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Knowledge Check

  • A reservoir is at 827^(@)C and Carnot's engine takes a thousand kilocalories of heat from it and exhausts it to a sink at 27^(@)C . What is the amount of work and the efficiency of the engine?

    A
    `2.7 xx10^(5)` cal, 70.70%
    B
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    C
    `2.70 xx 10^(5)` cal, 80.70%
    D
    `3.70 xx 10^(5)` cal, 70.70%

  • A heat engine takes in 300 K cal of heat from a reservoir at 627^(@)C and gives it to a sink at 27^(@)C . The work done by the engine is

    A
    `4.2xx10^(6)J`
    B
    `16.8xx10^(6)J`
    C
    `8.4xx10^(6)J`
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    `2.1xx10^(6)J`

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    A
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    C
    `6.27xx10^(5) cal`
    D
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