23. The Second Law of Thermodynamics

A theoretical heat engine in space could operate between the Sun's 5500°C surface and the –270.3°C temperature of intergalactic space. What would be its maximum theoretical efficiency?

A Carnot engine with an efficiency of 70% is cooled by water at 10°C. What temperature must the hot reservoir be maintained at?

Your friend claims they have a design for a reversible heat engine that can operate between the freezing and boiling temperatures of water that has an efficiency of 30%. Is this possible?

(II) 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.

(III) One mole of monatomic gas undergoes a Carnot cycle with T_H = 350°C and T_L = 210°C. The initial pressure is 8.8 atm. During the isothermal expansion, the volume doubles.

(c) Calculate the efficiency of the cycle using Eqs. 20–1 and 20–3.

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(III) A Carnot cycle, shown in Fig. 20–5, has the following conditions: Vₐ = 7.5 L , Vᵦ = 15.0L , T_H = 470°C and T_L = 260°C . The gas used in the cycle is 0.50 mol of a diatomic gas, γ = 1.4 . Calculate

(a) the pressures at a and b;

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