A Carnot engine operates between 235^∘ C and 115^∘ C, absorbing 6.30 ×10^4 J per cycle at the h

step 1 So here in this problem we are given that a Carnot heat engine works between temperature 235 deg

A Carnot engine operates between 235^∘ C and 115^∘ C,...

A Carnot engine operates between $235^{\circ} \mathrm{C}$ and $115^{\circ} \mathrm{C},$ absorbing $6.30 \times 10^{4} \mathrm{~J}$ per cycle at the higher temperature.
(a) What is the efficiency of the engine? (b) How much work per cycle is this engine capable of performing?

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Key Concepts

Work and Heat Relationship

The work performed by an engine is directly related to the input heat and its efficiency. Specifically, in the Carnot cycle, the work output per cycle is obtained by multiplying the efficiency by the heat absorbed from the high-temperature reservoir, linking thermal energy conversion to mechanical work.

Temperature Conversion from Celsius to Kelvin

In thermodynamics, it is essential to use Kelvin for temperature measurements because the efficiency formulas rely on absolute temperature. This involves adding 273.15 to the Celsius temperatures to convert them to Kelvin, ensuring accurate calculations in formulas like ? = 1 - (T_low/T_high).

Carnot Cycle

The Carnot cycle is an idealized thermodynamic cycle that provides the maximum possible efficiency a heat engine can achieve operating between two reservoirs. It is composed of two isothermal processes and two adiabatic processes, and it serves as a benchmark against which real engines are compared.

Heat Engine Efficiency

Efficiency in the context of heat engines is the ratio of the work output to the heat energy input. For the Carnot cycle, it is given by the formula ? = 1 - (T_low/T_high), where T_low and T_high are the absolute temperatures (in Kelvin) of the cold and hot reservoirs, respectively.

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