Tag: heat engines

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Multiple choice physics heat engine: second law of thermodynamics conversion of heat into work: heat engine and it's efficiency engines and cycles heat engines refrigerators and heat pumps

An engine has an efficiency of 0.25 when temperature of sink is reduced by 58C,if its efficiency is doubled, then the temperature of the source is:

  1. 150K

  2. 222K

  3. 242K

  4. 232K
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let us consider $T _1=$ temperature of the source

$T _2=$ temperature of the sink
The efficiency of the engine,
$0.25=1-\dfrac{T _2}{T _1}$
$\dfrac{T _2}{T _1}=0.75$
$T _2=0.75T _1$. . . . . . . . .(1)
When the temperature of the sink is reduced by $58^0C$, then the efficiency is double,
$2\times 0.25=1-\dfrac{T _2-58}{T _1}$
$\dfrac{T _2-58}{T _1}=0.5$
$T _2-58=0.5T _1$
$0.75T _1-58=0.5T _1$ .........(from equation 1)
$0.25T _1-58=0$
$0.25T _1=58$
$T _1=\dfrac{58}{0.25}$
$T _1=232 K$
The correct option is D.