The efficiency of a Carnot heat engine is 0.5 | vedclass

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

Question

(A) The efficiency $\eta$ of a Carnot heat engine is given by the formula: $\eta = 1 - \frac{T_{2}}{T_{1}}$.Given that $\eta = 0.5$, we have $0.5 = 1

Vedclass · Accepted Answer

$2 \,T_{1}, 2 \,T_{2}$

Vedclass · Answer

(A) The efficiency $\eta$ of a Carnot heat engine is given by the formula: $\eta = 1 - \frac{T_{2}}{T_{1}}$.Given that $\eta = 0.5$, we have $0.5 = 1 - \frac{T_{2}}{T_{1}}$, which implies $\frac{T_{2}}{T_{1}} = 0.5$, or $T_{1} = 2T_{2}$.For another Carnot engine to have the same efficiency of $0.5$, the ratio of the sink temperature to the source temperature must remain the same, i.e., $\frac{T_{2}'}{T_{1}'} = 0.5$.If we multiply both the source and sink temperatures by the same factor $k$, the new efficiency is $\eta' = 1 - \frac{k T_{2}}{k T_{1}} = 1 - \frac{T_{2}}{T_{1}} = 0.5$.Therefore, if the source temperature is $2T_{1}$ and the sink temperature is $2T_{2}$, the efficiency remains $0.5$.

The efficiency of a Carnot heat engine is $0.5$ when the temperature of the source is $T_{1}$ and that of the sink is $T_{2}$. The efficiency of another Carnot heat engine is also $0.5$. The temperatures of the source and sink of the second engine are respectively:

Similar Questions

Consider the given series combination of Carnot cycles. If $W_1 = W_2$,then the value of $T$ is ...... $K$ (all temperatures are maintained at their respective values).

$A$ Carnot engine $A$ working between temperatures $600 \ K$ and $T$ $(T < 600 \ K)$ and another Carnot engine $B$ working between temperatures $T$ $(T > 400 \ K)$ and $400 \ K$ are connected in series. If the work done by both the engines is the same, then $T =$ (in $K$)

Which statement is incorrect?

$A$ reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^\circ C$,the efficiency of the engine is doubled. The temperatures of the source and sink are:

The ratio of the efficiencies of two Carnot engines $A$ and $B$ is $1.25$. The temperature difference between the source and the sink is the same in both engines. The ratio of the absolute temperatures of the sources of engines $A$ and $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module