A reversible power cycle whose thermal efficiency is 40 % receives 50 kJ by heat transfer from

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A reversible power cycle whose thermal efficiency is 40 %...

A reversible power cycle whose thermal efficiency is $40 \%$ receives $50 \mathrm{~kJ}$ by heat transfer from a hot reservoir at $600 \mathrm{~K}$ and rejects energy by heat transfer to a cold reservoir at temperature $T_{\mathrm{C}}$. Determine the energy rejected, in $\mathrm{kJ}$, and $T_{\mathrm{C}}$, in $\mathrm{K}$.

Key Concepts

Thermal Efficiency

This concept measures the ratio of the work output of the cycle to the heat input. It is a fundamental parameter in thermodynamics that quantifies how effectively a system converts heat from a high-temperature reservoir into work, and it plays a critical role in comparing and analyzing different thermal systems.

Reversible Cycle

A reversible cycle is an idealized thermodynamic cycle that operates in such a way that all processes involved can be reversed without leaving any net changes in the system and surroundings. These cycles represent the maximum theoretical performance limits, as they assume no irreversibilities, such as friction or heat losses, thus providing benchmarks for real-world engines.

Carnot Efficiency

This is the efficiency of an idealized reversible engine operating between two thermal reservoirs, defined by the temperatures of these reservoirs. It sets the upper limit on the efficiency that any heat engine can achieve, demonstrating that efficiency is fundamentally limited by the temperature difference between the heat source and the sink.

Energy Balance in Thermodynamic Cycles

The energy balance principle states that the net heat input into a thermodynamic cycle equals the net work output plus the heat rejected. This balance, an application of the first law of thermodynamics, is critical for analyzing and designing power cycles by relating the energy input, useful work produced, and energy discharged to the surroundings.

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