Question

In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of $7 \times 10^{8} \mathrm{~K}$. If this gas could be used to operate a Carnot engine with $T_{\mathrm{L}}=100^{\circ} \mathrm{C},$ what would be the engine's efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

Name: Problem 26, Chapter 20: Fundamentals of Physics
Uploaded: 2021-07-13T16:36:17-08:00
Duration: 1 min 27 s
Channel: Vipender Yadav
Description: In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of 7 ×10^8 K. If this gas could be used to operate a Carnot engine with TL=100^∘ C, what would be the engine's efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

    In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of $7 \times 10^{8} \mathrm{~K}$. If this gas could be used to operate a Carnot engine with $T_{\mathrm{L}}=100^{\circ} \mathrm{C},$ what would be the engine's efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

Fundamentals of Physics

David Halliday,… 11th Edition

Chapter 20, Problem 26

Instant Answer

Solved by Expert Vipender Yadav

07/13/2021

Step 1

We can do this by adding 273.15 to the given temperature: $T_L = 100^{\circ} \mathrm{C} + 273.15 = 373.15 \mathrm{K}$ Now, we can use the formula for the efficiency of a Carnot engine: $\eta = 1 - \frac{T_L}{T_H}$ where $\eta$ is the efficiency, $T_L$ is the Show more…

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In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of $7 \times 10^{8} \mathrm{~K}$. If this gas could be used to operate a Carnot engine with $T_{\mathrm{L}}=100^{\circ} \mathrm{C},$ what would be the engine's efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

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Key Concepts

Carnot Efficiency

The Carnot efficiency represents the maximum possible efficiency that any heat engine can achieve operating between two temperature reservoirs. It is derived from the second law of thermodynamics and is defined by the formula ? = 1 - T_cold/T_hot, where both temperatures must be in an absolute scale (e.g., Kelvin). This concept is fundamental in understanding the limitations of thermal engines and serves as an idealized benchmark for real engines.

Absolute Temperature Conversion

When performing thermodynamic calculations, it is essential to use temperatures measured on an absolute scale, such as Kelvin, because the formulas, including that for Carnot efficiency, rely on absolute temperature differences. Converting temperatures from scales like Celsius to Kelvin ensures that the computations correctly reflect the thermal properties needed for accurate assessments in energy systems.

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