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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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