Question

Each of two Carnot X and Y engines uses the same cold reservoir at a temperature of 400 o

F for its exhaust heat. X engine receives 

twice the heat input of Y engine as 1450 J. The work from either of these engines is used to drive a pulley arrangement that uses a 

rope to accelerate a 125-kg crate from rest along a horizontal frictionless surface. With engine X the crate attains a speed of 20.00 

km/s; while with engine 2 it attains a speed of 30.00 m /hr. (i) With which engine is the change in the crate’s kinetic energy greater? 

(ii) Which engine does more work? (iii) For which engine is 

Answer 1

$E=\frac{mv^2}{2},\implies E\sim v^2,$

$v_X=20~\frac{km}{s}>30~\frac{m}{hr}=v_Y,$ so

$E_X>E_Y$ and $A_X>A_Y.$