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Ch. 20 - Second Law of Thermodynamics
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 20 - Second Law of ThermodynamicsProblem 20c
Chapter 20, Problem 20c

One mole of monatomic gas undergoes a Carnot cycle with TH = 350°C and TL = 210°C. The initial pressure is 8.8 atm. During the isothermal expansion, the volume doubles. Calculate the efficiency of the cycle using Eqs. 20–1 and 20–3.

Verified step by step guidance
1
Convert the given temperatures from Celsius to Kelvin, as thermodynamic calculations require absolute temperature. Use the formula: T(K) = T(°C) + 273.15. For T_H = 350°C and T_L = 210°C, calculate T_H and T_L in Kelvin.
Recall the formula for the efficiency of a Carnot cycle: η = 1 - (T_L / T_H). Substitute the values of T_H and T_L (in Kelvin) into this equation to calculate the efficiency.
Understand that the efficiency η is a dimensionless quantity, often expressed as a percentage. Multiply the result by 100 to express the efficiency as a percentage.
Review the assumptions of the Carnot cycle: it is an idealized process with no energy losses, and the efficiency depends only on the temperatures of the hot and cold reservoirs.
Ensure that the calculated efficiency is reasonable and consistent with the second law of thermodynamics, which states that no heat engine can be 100% efficient unless T_L = 0 K.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between two temperature reservoirs. It consists of four reversible processes: two isothermal (constant temperature) and two adiabatic (no heat exchange). Understanding this cycle is crucial for calculating the efficiency of real engines and serves as a benchmark for performance.
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The Carnot Cycle and Maximum Theoretical Efficiency

Thermal Efficiency

Thermal efficiency is defined as the ratio of the work output of a heat engine to the heat input from the hot reservoir. For a Carnot engine, it can be calculated using the formula η = 1 - (T_L / T_H), where T_L and T_H are the absolute temperatures of the cold and hot reservoirs, respectively. This concept is essential for evaluating how effectively a heat engine converts heat into work.
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Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, and temperature of an ideal gas through the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law is fundamental in thermodynamics for understanding the behavior of gases during various processes, including isothermal expansion in the Carnot cycle.
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Related Practice
Textbook Question

An ideal heat pump is used to maintain the inside temperature of a house at Tᵢₙ = 22°C when the outside temperature is Tₒᵤₜ. Assume the heat pump does work at a rate of 1700 W. Also assume that the house loses heat via conduction through its walls and other surfaces at a rate given by ( 650 W/C°) (Tᵢₙ - Tₒᵤₜ). If the outside temperature is less than you just calculated, what happens?

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Textbook Question

(II) What is the temperature inside an ideal refrigerator–freezer that operates with a COP = 7.0 in a 22°C room?

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Textbook Question

One mole of monatomic gas undergoes a Carnot cycle with TH = 350°C and TL = 210°C. The initial pressure is 8.8 atm. During the isothermal expansion, the volume doubles. Find the values of the pressure and volume at the points a, b, c, and d of Fig. 20–5.

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Textbook Question

(II) 1.00 mole of nitrogen (N₂) gas and 1.00 mole of argon (Ar) gas are in separate, equal-sized, insulated containers at the same temperature. The containers are then connected and the gases (assumed ideal) allowed to mix. What is the change in entropy

(a) of the system

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Textbook Question

What is the coefficient of performance of an ideal heat pump that extracts heat from 6°C air outside and deposits heat inside a house at 24°C?

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Textbook Question

The working substance of a certain Carnot engine is 1.0 mol of an ideal monatomic gas. During the isothermal expansion portion of this engine’s cycle, the volume of the gas doubles, while during the adiabatic expansion the volume increases by a factor of 6.2. The work output of the engine is 920 J in each cycle. Compute the temperatures of the two reservoirs between which this engine operates.