A heat engine has an efficiency of frac{1}{6} | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the source temperature and $T_2$ is the sink temperature

Vedclass · Accepted Answer

$99$

Vedclass · Answer

(B) The efficiency of a Carnot engine is given by $\eta = 1 - \frac{T_2}{T_1}$,where $T_1$ is the source temperature and $T_2$ is the sink temperature in Kelvin.In the first case,$\eta_1 = \frac{1}{6} = 1 - \frac{T_2}{T_1}$,which implies $\frac{T_2}{T_1} = \frac{5}{6}$ (Equation $i$).In the second case,the sink temperature is reduced by $62^{\circ}C$ (which is equivalent to $62 K$ in temperature difference),so the new sink temperature is $T_2' = T_2 - 62$. The new efficiency is $\eta_2 = 2 	imes \frac{1}{6} = \frac{1}{3}$.Thus,$\frac{1}{3} = 1 - \frac{T_2 - 62}{T_1}$,which implies $\frac{T_2 - 62}{T_1} = \frac{2}{3}$ (Equation $ii$).Subtracting Equation $ii$ from Equation $i$: $\frac{T_2}{T_1} - \frac{T_2 - 62}{T_1} = \frac{5}{6} - \frac{2}{3}$.$\frac{62}{T_1} = \frac{5-4}{6} = \frac{1}{6}$.Therefore,$T_1 = 62 	imes 6 = 372 K$.To convert Kelvin to Celsius: $T(^{\circ}C) = 372 - 273 = 99^{\circ}C$.

$A$ heat engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62^{\circ}C$,its efficiency gets doubled. The temperature of the source is $.....^{\circ}C$.

Similar Questions

Explain: Carnot cycle and Carnot engine.

An engine operating between the boiling and freezing points of water will have:
$1.$ Efficiency more than $27 \%$
$2.$ Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
$3.$ Efficiency equal to $27 \%$
$4.$ Efficiency less than $27 \%$

$A$ Carnot engine operates between $300 \ K$ and $600 \ K$. If the work done per cycle is $800 \ J$,then the heat supplied per cycle is ....... $J/cycle$.

$A$ Carnot engine operating between temperatures $T_1$ and $T_2$ has an efficiency of $\frac{1}{6}$. When $T_2$ is lowered by $62\, K$,its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are,respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module