An ideal heat engine working between T1 and T2 has an efficiency η. When T1 is doubled and T2 is halved, efficiency becomes/remains (T1>T2)

η=1−T2T1η'=1−0.5T22T1=1−0.25T2T1After solving,η'=η+34

An ideal heat engine working between T1 and T2 has an efficiency η. When T1 is doubled and T2 is halved, efficiency becomes/remains (T1>T2)

η=1−T2T1η'=1−0.5T22T1=1−0.25T2T1After solving,η'=η+34

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An ideal heat engine working between T₁ and T₂ has an efficiency $η$ . When T₁ is doubled and T₂ is halved, efficiency becomes/remains $(T_{1} > T_{2})$

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$η$

$\frac{4 + η}{3}$

$\frac{η + 3}{4}$

$\frac{η}{4}$

answer is C.

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Detailed Solution

$η = 1 - \frac{T_{2}}{T_{1}}$

$η' = 1 - \frac{{0.5T}_{2}}{{2T}_{1}} = 1 - \frac{{0.25T}_{2}}{T_{1}}$

After solving,

$η' = \frac{η + 3}{4}$

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An ideal heat engine working between T1 and T2 has an efficiency η. When T1 is doubled and T2 is halved, efficiency becomes/remains (T1>T2)

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An ideal heat engine working between T₁ and T₂ has an efficiency $η$ . When T₁ is doubled and T₂ is halved, efficiency becomes/remains $(T_{1} > T_{2})$