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Q.

Carnot engine takes one thousand kilo calories of heat from a reservoir 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?

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a

W=4.18×105cal

η=  52.72%

b

W=6.18×105cal

η=  72.53%

c

W=7.28×105cal

η=  72.72%

d

W=8.41×105cal

η=  42.32%

answer is C.

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Detailed Solution

Given, Q1=106cal

T1=(827+273)=1100K

T2=(27+273)=300K

Q2Q1=T2T1Q2=T2T1·Q1=3001100106

=2.72×105cal

W=Q1-Q2=7.28×105cal

and

as,

Efficiency of the cycle,

η=1-T2T1×100 or   η=1-3001100×100

=72.72%

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Carnot engine takes one thousand kilo calories of heat from a reservoir 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?