(a) How much heat transfer occurs to the environment by an...

(a) How much heat transfer occurs to the environment by an electrical power station that uses $1.25 \times 10^{14}$ J of heat transfer into the engine with an efficiency of 42.0$\% ?$ (b) What is the ratio of heat transfer to the environment to work output? (c) How much work is done?

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Key Concepts

Thermal Efficiency

Thermal efficiency is a measure of how effectively a heat engine converts the input heat energy into useful work. It is defined as the ratio of work output to the heat input, indicating the fraction of energy that is successfully transformed into work rather than being lost to the surroundings.

Heat Transfer

Heat transfer in the context of thermal systems refers to the energy exchanged between the system and its environment. In heat engines, a portion of the absorbed heat is rejected to the environment, which is a key factor in determining the overall efficiency and performance of the engine.

Work Output

Work output represents the useful energy that is produced by the engine from the heat input. It is calculated using the efficiency of the engine and serves as a measure of how much of the input energy is accurately converted into mechanical or electrical energy.

Energy Conservation

Energy conservation, rooted in the first law of thermodynamics, states that the total energy input into a system must equal the sum of the work output and the energy rejected. This principle is critical for analyzing energy processes, ensuring that all energy transformations within the system are accounted for.

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