Suppose a heat engine is connected to two energy reservoirs,...

Suppose a heat engine is connected to two energy reservoirs, one a pool of molten aluminum $\left(660^{\circ} \mathrm{C}\right)$ and the other a block of solid mercury $\left(-38.9^{\circ} \mathrm{C}\right) .$ The engine runs by freezing $1.00 \mathrm{g}$ of aluminum and melting $15.0 \mathrm{g}$ of mercury during each cycle. The heat of fusion of aluminum is $3.97 \times 10^{5} \mathrm{J} / \mathrm{kg}$; the heat of fusion of mercury is $1.18 \times 10^{4} \mathrm{J} / \mathrm{kg} .$ What is the efficiency of this engine?

Key Concepts

Thermodynamic Efficiency

This concept describes the ratio of the useful work output of a heat engine to the heat energy extracted from the hot reservoir. It quantifies how effectively the engine converts thermal energy into mechanical work, using the relationship efficiency = work output divided by heat input.

Latent Heat and Phase Changes

Latent heat is the energy absorbed or released by a substance during a phase change at a constant temperature. In the context of heat engines, phase transitions such as melting or freezing provide a fixed amount of energy transfer per unit mass, which is critical for calculating the energy flows during each cycle.

Energy Conservation in Heat Engines

This fundamental principle states that the total energy input into a system must equal the sum of the work output and the energy rejected to the cold reservoir. In heat engine problems, energy conservation is used to balance the heat exchanges resulting from different processes, such as phase changes, ensuring a consistent accounting of energy.

Temperature Scales in Thermodynamics

Thermodynamic analyses require the use of absolute temperature scales, typically Kelvin, to ensure accurate calculations of efficiencies and work. The temperatures of the heat reservoirs set the limits for possible energy conversion, influencing factors such as theoretical maximum efficiency (e.g., Carnot efficiency), even if the process itself involves non-ideal steps like phase changes.

Transcript

Please give Ace some feedback