Each of two Carnot engines uses the same cold reservoir at a temperature of 287

Question

Each of two Carnot engines uses the same cold reservoir at a temperature of 287 K for its exhaust heat. Each engine receives 1440 in J of input heat. The work from either of these engines is used to drive a pulley arrangement that uses a rope to accelerate a 124-kg crate from rest along a horizontal frictionless surface, as shown in the figure. With engine 1 the crate attains a speed of 2.10 m/s, while with engine 2 it attains a speed of 3.10 m/s. Find the temperature of the hot reservoir for (a) engine 1 and (b) engine 2.

Explanation / Answer

(A) engine 1:
  
W = delta(KE) = 124 x 2.10^2 /2  

W = 273.42 J  

n = W / Qin = 1 - (T_cold / T_hot)  

273.42 / 1440 = 1 - (287 / T_hot)

T_hot = 354 K  

(B) W = 124 x 3.10^2 /2 = 595.82 J  

595.82 / 1440 = 1 - (287 / T_hot)

T_hot = 490 K

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.