Tag: heat engines

Questions Related to heat engines

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:

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

  1. 150K

  2. 222K

  3. 242K

  4. 232K

Show answer
Correct Option: D
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.