How Does a Heat Engine Lift a Mass Efficiently?

In summary, the problem involves a heat engine operating between temperatures of 500 K and 300 K to lift a 10-kilogram mass at a constant speed of 4 meters per second. The power that the engine must supply to lift the mass can be found using the equation W = F*v, where F is the force and v is the velocity. The maximum possible efficiency of the engine can be determined by using the equation Efficiency = Output power / Input power. If the engine were to operate at maximum possible efficiency, the rate at which the hot reservoir supplies heat to the engine and the rate at which heat is exhausted to the cold reservoir can be found.
  • #1
CloCon
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Homework Statement


A heat engine operating between temperatures of 500 K and 300 K is used to lift a 10-kilogram mass vertically at a constant speed of 4 meters per second.

(a) Determine the power that the engine must supply to lift the mass.

(b) Determine the maximum possible efficiency at which the engine can operate.

(c) If the engine were to operate at maximum possible efficiency, determine the following:

i. The rate at which the hot reservoir supplies heat to the engine
ii. The rate at which heat is exhausted to the cold reservoir

Homework Equations


F = ma
W = FD
Pavg = Change in Work / Change in Time


The Attempt at a Solution



(a) F = ma
F = 10 kg * 9.8 m/s^2
F = 98 N

How can I find power without being given a displacement? Power is a function of work and time, and work is a function of force and displacement - All I have is force.

Solution attempts for B and C forthcoming when I figure out A.
 
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  • #2
Output power also defined as W = F*v, where v is the velocity.
Temperatures of the source and sink is given.Find the efficiency of the engine.
Efficiency = Output power/Input power.
 

1. How does a heat engine lift a mass?

A heat engine lifts a mass by converting thermal energy into mechanical energy. This is done through a series of thermodynamic processes, such as heating and expanding a gas, which then drives a piston or turbine to perform work and lift the mass.

2. What is the efficiency of a heat engine lifting a mass?

The efficiency of a heat engine lifting a mass depends on various factors, such as the temperature difference between the heat source and sink, the type of engine, and the amount of heat energy supplied. According to the Carnot efficiency formula, the maximum theoretical efficiency of a heat engine is determined by the ratio of the temperature difference between the heat source and sink.

3. Is a heat engine lifting a mass a reversible process?

No, a heat engine lifting a mass is not a reversible process. This is because it involves the conversion of heat energy into mechanical work, which is subject to the second law of thermodynamics. This law states that heat can only flow from a hot object to a cold object, and not vice versa, resulting in an irreversible process.

4. What are the different types of heat engines used to lift a mass?

There are various types of heat engines that can be used to lift a mass, such as steam engines, gas turbines, Stirling engines, and internal combustion engines. Each type operates on different thermodynamic principles and has its own advantages and applications.

5. Can a heat engine lifting a mass be used for practical applications?

Yes, heat engines lifting a mass have numerous practical applications, such as in power plants, transportation vehicles, and industrial machinery. These engines are efficient and reliable sources of mechanical work, making them essential for various industries and everyday life.

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