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Heat and Thermodynamics question

2013 · Q160
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Heat and Thermodynamics question

2013 · Q160

NEETPhysicsHeat and ThermodynamicsMCQ+4 / −1
Two Carnot engines A and B are operated in series. The engine A receives heat from the source at temperature T1 and rejects the heat to the sink at temperature T. The second engine B receives the heat at temperature T and rejects to its sink at temperature T2. For what values of T the efficiencies of the two engines are equal
  1. A
    T1−T22{{{T_1} - {T_2}} \over 2}2T1​−T2​​
  2. B
    T1T2{T_1}{T_2}T1​T2​
  3. C
    T1T2\sqrt {{T_1}{T_2}}T1​T2​​
  4. D
    T1+T22{{{T_1} + {T_2}} \over 2}2T1​+T2​​
View written solutionFree

Correct answer: C

Efficiency of engine A, η1=1−TT1{\eta _1} = 1 - {T \over {{T_1}}}η1​=1−T1​T​

Efficiency of engine B, η2=1−T2T{\eta _2} = 1 - {{{T_2}} \over T}η2​=1−TT2​​

Here, η1=η2{\eta _1} = {\eta _2}η1​=η2​

∴TT1=T2T⇒T=T1T2\therefore {T \over {{T_1}}} = {{{T_2}} \over T} \Rightarrow T = \sqrt {{T_1}{T_2}}∴T1​T​=TT2​​⇒T=T1​T2​​

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