By operating a reversible heat engine with an ideal gas as the working substance in a Carnot cycle and measuring the ratio Q_c/Q_h, we can calculate A) n, the number of moles of the ideal gas. B) the ratio V_c/V_h of the volumes of the ideal gas. C) the ratio P_c/P_h of the pressures of the ideal gas. D) the ratio P_cV_c/P_hV_h of the products of volumes and pressures of the ideal gas. E) the value of Avogadro's number.

Question

Quizplus · Accepted Answer

The given ratio can be written as (QC/QH)(U1B0/U1B1cS1)(U1B1hS1/U1B0)(V_c/V_h)(P_c/P_h). Since Carnot cycle is a reversible cycle, the efficiencies of the engine are equal to (Qin - Qout)/Qin where Q is the heat absorbed/rejected and are proportional to the temperature differences of the heat reservoirs, and (U1 - U0)/Qin and (U1 - U0)/Qout where U is the internal energy of the gas. As a result, the ratio (QC/QH)(U1B0/U1B1cS1)(U1B1hS1/U1B0) is equal to the ratio (V_c/V_h)(P_c/P_h) and is dependent only on the temperature of the heat reservoirs, regardless of the nature of the working substance. Therefore, the only possible result that can be calculated from the given ratio is the ratio of the products of volumes and pressures, P_cV_c/P_hV_h.

By Operating a Reversible Heat Engine with an Ideal Gas