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

(a) Show that the work done by a Carnot engine is equal to the area enclosed by the Carnot cycle on a PV diagram, Fig. 20–5. (See Section 19–7.) (b) Generalize this to any reversible cycle.

(III) A Carnot cycle, shown in Fig. 20–5, has the following conditions: V_a = 7.5 L, V_b = 15.0 L, 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 the pressures at a and b.

(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. Determine Q, W, and ∆E_int for each segment of the cycle.

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?