A nuclear power plant has a maximum steam temperature (TH) of 310^∘ C. It produces 650 MW of ele

step 1 In this problem we are given there are two parts in the first part we are given the temperature

A nuclear power plant has a maximum steam temperature (TH)...

A nuclear power plant has a maximum steam temperature $\left(T_{\mathrm{H}}\right)$ of $310^{\circ} \mathrm{C}$. It produces $650 \mathrm{MW}$ of electric power in the winter, when its $T_{\mathrm{C}}$ is effectively $0^{\circ} \mathrm{C}$. (a) Find its maximum winter efficiency. (b) If its summertime $T_{\mathrm{C}}$ is $38^{\circ} \mathrm{C},$ what's its summertime electric power output, assuming nothing else changes?

A nuclear power plant has a maximum steam temperature $\left(T_{\mathrm{H}}\right)$ of $310^{\circ} \mathrm{C}$. It produces $650 \mathrm{MW}$ of electric power in the winter, when its $T_{\mathrm{C}}$ is effectively $0^{\circ} \mathrm{C}$.
(a) Find its maximum winter efficiency. (b) If its summertime $T_{\mathrm{C}}$ is $38^{\circ} \mathrm{C},$ what's its summertime electric power output, assuming nothing else changes?

Key Concepts

Efficiency and Power Output Relationship

In thermodynamic systems like power plants, the efficiency determines how much of the input thermal energy is converted into useful work, such as electricity. A change in the temperature of the cold reservoir, for example, alters the maximum achievable efficiency given by the Carnot limit, which in turn affects the maximum electric power output if the thermal input power remains constant. This concept links the performance of thermal cycles directly to their operating temperature conditions.

Carnot Efficiency

Carnot efficiency is a theoretical upper limit on the efficiency of a heat engine operating between two temperatures. It is given by the formula ? = 1 - (T_C / T_H), where T_H and T_C are the absolute temperatures (in Kelvin) of the hot and cold reservoirs, respectively. This concept is fundamental in thermodynamics as it sets the maximum possible efficiency that any real engine can achieve under idealized reversible conditions.

Temperature Conversion

Converting temperatures from Celsius to Kelvin is essential when applying thermodynamic formulas such as the Carnot efficiency formula. Since the Kelvin scale is an absolute temperature scale, it correctly accounts for the physical property that all thermodynamic temperatures must be positive, ensuring valid and meaningful calculations for heat engine efficiency.

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