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A Carnot engine takes 3xx10^6 cal of hea...

A Carnot engine takes `3xx10^6` 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

(a)`4.2 xx 10^(6)J`

B

(b)`8.4 xx 10^(6)J`

C

(c)`16.8 xx 10^(6)J`

D

(d)`zero`

Text Solution

Verified by Experts

The correct Answer is:
B
`T_("source") = 627^(@)C = 627 + 273 = 900K`
`T_("sink") = 27^(@)C = 27 + 273 = 300K`
Efficiency `(eta)= 1 - (T_("sink"))/(T_("source")) = 1-(300)/(900) = 1- (1)/(3)`
`(eta) = (2)/(3) = ("Output")/("Input") = ("Work")/(Heat Input")`
`implies (2)/(3) xx "Heat Input" = "Work"`
`implies (2)/(3) xx 3xx10^(6) xx 4.2 = "Work"`
`implies "Work" = 8.4 xx 10^(6)J`
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