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MCA Mild/Moderate Science (054) Practice Tests & Test Prep by Exam Edge - Review



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MCA Mild/Moderate Middle/Secondary Multi-Content Science - Reviews


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Based on 125 reviews


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See why our users from 154 countries love us for their exam prep! Including 125 reviews for the MCA Mild/Moderate Science exam.

Exam Edge is an industry leader in online test prep. We work with institutional partners to offer a wide array of practice tests that will help you prepare for your big exam. No matter how niche your field of interest might be, we're here to help you prepare for test day.

   Excellent -- Based on 125 reviews

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MCA Mild/Moderate Middle/Secondary Multi-Content Science - Test Reviews Sample Questions

If the temperature of the cold reservoir is Tc and the temperature of the hot reservoir is Th, what is the maximum efficiency of an operating heat engine?

Correct Answer:
1- tc / th
the maximum efficiency of an operating heat engine when the temperature of the cold reservoir is \( t_c \) (in kelvin) and the temperature of the hot reservoir is \( t_h \) (in kelvin) can be determined using the principles of thermodynamics, specifically by considering the efficiency of a carnot engine. the carnot engine, conceptualized by sadi carnot in the 19th century, represents an idealized heat engine with the maximum possible efficiency.

carnot's theorem states that no heat engine operating between two heat reservoirs can be more efficient than a carnot engine operating between those same reservoirs. this is a fundamental result derived from the second law of thermodynamics, which implies that all real heat engines have efficiencies less than or equal to that of a carnot engine under the same conditions.

the efficiency (\( \eta \)) of a carnot engine is given by the formula: \[ \eta = 1 - \frac{t_c}{t_h} \] where \( t_c \) is the absolute temperature of the cold reservoir and \( t_h \) is the absolute temperature of the hot reservoir. this equation reveals that the efficiency of a carnot engine depends solely on the temperatures of the hot and cold reservoirs and not on the specific type of working substance or the details of the engine operation.

the formula \( 1 - \frac{t_c}{t_h} \) indicates that the efficiency increases as \( t_c \) decreases or as \( t_h \) increases. in practical terms, this means that to achieve higher efficiencies, an engine should operate between a very hot heat source and a very cold sink. however, there are practical limits to how hot the heat source can be and how cold the heat sink can be, constrained by material properties and environmental considerations.

it is important to note that while the carnot cycle offers a theoretical maximum efficiency, actual engines cannot achieve this efficiency due to various real-world factors such as friction, unrecoverable heat losses, and the non-ideal behavior of working fluids. nonetheless, the carnot efficiency serves as a crucial benchmark for evaluating the performance of practical heat engines and inspires the design of more efficient thermal systems.