Each of two Carnot engines uses the same cold reservoir at a temperature of 275
ID: 1469003 • Letter: E
Question
Each of two Carnot engines uses the same cold reservoir at a temperature of 275 K for its exhaust heat. Each engine receives 1400 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 125-kg crate from rest along a horizontal frictionless surface, as shown in the figure. With engine 1 the crate attains a speed of 1.80 m/s, while with engine 2 it attains a speed of 4.00 m/s
Find the temperature of the hot reservoir for each engine (In KELVINS)
TH,1 = TH,2 =Explanation / Answer
TC1 = TC2 = 275 k
Qin1 = Qin2 = 1400 J
Workdone by first engine = 0.5*m*v1^2
= 0.5*125*1.8^2
= 202.5 J
efficiency of first engine, e1 = 1 - TC1/TH1
Workdone/Qin = 1 - 275/TH1
202.5/1400 = 1 - 275/TH1
0.14464 = 1 - 275/TH1
275/TH1 = 1 - 0.14464
TH1 = 275/(1 - 0.14464)
= 321.5 K <<<<<<<<<<<<<<<<<<<<--------------------------Answer
Workdone by second engine = 0.5*m*v2^2
= 0.5*125*4^2
= 1000 J
efficiency of seond engine, e1 = 1 - TC2/TH2
Workdone/Qin = 1 - 275/TH2
1000/1400 = 1 - 275/TH2
0.714 = 1 - 275/TH2
275/TH2 = 1 - 0.714
TH2 = 275/(1 - 0.714)
= 961.5 K <<<<<<<<<<<<<<<<<<<<--------------------------Answer
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