Two ideal Carnot engines operate in cascade (all heat given up by one engine is used…

PHYSICS · Single correct · A Level · Physics · Engineering physics · Engineering physics

Problem

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures,

T_1

and

T_2

. The temperature of the hot reservoir of the first engine is

T_1

and the temperature of the cold reservoir of the second engine is

T_2

T

is temperature of the sink of first engine which is also the source for the second engine. How is

T

related to

T_1

and

T_2

, if both the engines perform equal amount of work ? (1)

T = \frac{2T_1T_2}{T_1 + T_2}

(2)

T = \frac{T_1 + T_2}{2}

(3)

T = \sqrt{T_1T_2}

(4)

T = 0