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An ideal Carnot heat engine with an effi...

An ideal Carnot heat engine with an efficiency of `30%`. It absorbs heat from a hot reservoir at `727^(@)C`. The temperature of the cold reservoir is

A

`509^(@)C`

B

`427^(@)C`

C

`273^(@)C`

D

`218^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
`eta = 1 - (T_(C))/(T_(H)) implies 0.3 = 1 - (T_(C))/(1000)`
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The efficiency of a heat engine is defined as the ratio of the mechanical work done by the engine in one cycle to the heat absorbed from the high temperature source . eta = (W)/(Q_(1)) = (Q_(1) - Q_(2))/(Q_(1)) Cornot devised an ideal engine which is based on a reversible cycle of four operations in succession: isothermal expansion , adiabatic expansion. isothermal compression and adiabatic compression. For carnot cycle (Q_(1))/(T_(1)) = (Q_(2))/(T_(2)) . Thus eta = (Q_(1) - Q_(2))/(Q_(1)) = (T_(1) - T_(2))/(T_(1)) According to carnot theorem "No irreversible engine can have efficiency greater than carnot reversible engine working between same hot and cold reservoirs". Efficiency of a carnot's cycle change from (1)/(6) to (1)/(3) when source temperature is raised by 100K . The temperature of the sink is-

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ALLEN -GEOMETRICAL OPTICS-EXERCISE -01
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