Question

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water...

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 4.30×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water. During this time, how much work W is performed by the engine?

0 0
Add a comment Improve this question Transcribed image text
Answer #1

The heat delivered to the ice equals mass of malted ice times heat of fusion:
Qc = m∙∆Lf = 4.30×10-^2 kg *3.34×10^5 J /kg = 14362 J

Assuming stationary operation the net energy by work and heat to the engine is zero.
That means the heat absorbed from hot reservoir equals the work done by the engine plus the heat rejected to cold reservoir:
Q_h = Q_c + W
W = Q_h - Q_c

Moreover stationary operation requires that net entropy change of the engine during the process is zero. A Carnot engine operates reversibly, i.e.no entropy is produced in the process. Hence the entropy rise due to absorption of heat from hot reservoir equals entropy loss due to heat rejection:

Q_h/T_h = Q_c/T_c
Q_h = (T_h/T_c)∙Q_c

Therefore
W = (T_h/T_c)∙Q_c - Q_c

W = [(T_h/T_c) - 1]∙Q_c
W = [(373K/273K) - 1]*14362 J
W = 5260.80J


Add a comment
Know the answer?
Add Answer to:
A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water...

    A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 5.45×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water. A.) During this time, how much work W is performed by the engine?

  • A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water...

    A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 9.0 minutes of operation, the heat rejected by the engine melts 0.0520 kg of ice. During this time, how much work W is performed by the engine?

  • Chi c le X ROC a Am X BU X Aus x a Am X Net...

    Chi c le X ROC a Am X BU X Aus x a Am X Net x = 22 x Spex = Au x E c session.masteringphysics.com/myct/itemView?assignment ProblemiD=121987089 <Graded Tutorial for Monday Nov. 18 Melting Ice with a Carnot Engine Part A A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the...

  • 1. A Carnot engine has a hot reservoir at 250 degrees C, and a a cold...

    1. A Carnot engine has a hot reservoir at 250 degrees C, and a a cold reservoir at 25.0 degrees C. What is the efficiency of this engine? A) 10% B) 43% C) 57% D) 90% 2. A heat engine does 50 J of work and dumps 30 J of heat into the cold reservoir. How much heat was absorbed from the hot reservoir? A) 20 J B) 30 J C) 50 J D) 80 J 3. A heat engine...

  • A Carnot engine has an efficiency of 0.445, and the temperature of its cold reservoir is...

    A Carnot engine has an efficiency of 0.445, and the temperature of its cold reservoir is 434 K. (a) Determine the temperature of its hot reservoir. (b) If 5610 J of heat is rejected to the cold reservoir, what amount of heat is put into the engine?

  • [3] A heat engine is reported to operate with 25 % efficiency when the cold reservoir...

    [3] A heat engine is reported to operate with 25 % efficiency when the cold reservoir is at 0° C. (a) Assuming this engine follows the Carnot cycle, what is the temperature of the hot reservoir? (b) Suppose the heat input to this engine was 10 J. Calculate the work done by this engine c) Suppose the heat input to this engine was 5). Calculate the heat rejected by this engine.

  • An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid...

    An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0∘C and rejects heat to a room at a temperature of 24.5 ∘C. Suppose that liquid water with a mass of 84.4 kg at 0.0∘C is converted to ice at the same temperature. Take the heat of fusion for water to be Lf = 3.34×105 J/kg . Part A How much heat |QH| is rejected to the room? Express your answer in...

  • An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid...

    An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0 ∘C and rejects heat to a room at a temperature of 21.6 ∘C. Suppose that liquid water with a mass of 77.6 kg at 0.0 ∘C is converted to ice at the same temperature. Take the heat of fusion for water to be Lf = 3.34×105 J/kg . |QH| | Q H | = 2.797×107 J How much energy E must...

  • Problem 18.46 An engine receives 790J of heat from a hot reservoir and gives off 450J...

    Problem 18.46 An engine receives 790J of heat from a hot reservoir and gives off 450J of heat to a cold reservoir. Part A What is the work done? ANSWER: W =   J   Part B What is the efficiency of this engine? ANSWER: e =

  • Suppose that there are two very large reservoirs of water, one at a temperature of 95.0...

    Suppose that there are two very large reservoirs of water, one at a temperature of 95.0 °C and one at a temperature of 17.0 °C. These reservoirs are brought into thermal contact long enough for 42130 J of heat to flow from the hot water to the cold water. Assume that the reservoirs are large enough so that the temperatures do not change significantly. What is the total change in entropy resulting from this heat exchange between the hot water...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT