A Carnot engine takes 3 ×10^6 cal of heat from a reservoir at 627^∘ C, and gives to a sink at 27

step 1 Hello students in the question it is given that a Carnot engine takes 3 into 10 to the power 6 c

A Carnot engine takes 3 ×10^6 cal of heat from a reservoir...

A Carnot engine takes $3 \times 10^{6}$ cal of heat from a reservoir at $627^{\circ} \mathrm{C}$, and gives to a sink at $27^{\circ} \mathrm{C}$. The work done by the engine is (A) $4.2 \times 10^{6} \mathrm{~J}$ (B) $16.8 \times 10^{6} \mathrm{~J}$ (C) $8.4 \times 10^{6} \mathrm{~J}$ (D) Zero

A Carnot engine takes $3 \times 10^{6}$ cal of heat from a reservoir at $627^{\circ} \mathrm{C}$, and gives to a sink at $27^{\circ} \mathrm{C}$. The work done by the engine is
(A) $4.2 \times 10^{6} \mathrm{~J}$
(B) $16.8 \times 10^{6} \mathrm{~J}$
(C) $8.4 \times 10^{6} \mathrm{~J}$
(D) Zero

Key Concepts

Work Calculation in Thermodynamic Cycles

The work done by a heat engine can be calculated by multiplying the input heat by the engine's efficiency. This concept demonstrates the direct relationship between the heat supplied, the efficiency derived from the temperature difference of the reservoirs, and the work output of the engine.

Carnot Engine

A Carnot engine is an idealized heat engine that operates on a reversible cycle, achieving the maximum possible efficiency between two thermal reservoirs. It establishes the theoretical upper limit on the efficiency that any heat engine can achieve, illustrating why real engines are less efficient.

Temperature Conversion

Thermodynamic calculations require temperatures to be expressed in an absolute scale, typically in Kelvin. Converting from Celsius to Kelvin is essential to correctly apply formulas such as the Carnot efficiency, ensuring the computed results are physically meaningful.

Carnot Efficiency

The efficiency of a Carnot engine is determined solely by the temperatures of its heat reservoirs, given by the formula ? = 1 - (T_cold/T_hot), where both temperatures are in Kelvin. This concept underlines the theoretical efficiency limit imposed by the second law of thermodynamics.

Energy Conversion

In thermodynamic calculations, energy might be provided in various units, such as calories or Joules. Converting between these units, for example using the conversion factor where one calorie equals approximately 4.184 Joules, is necessary for consistency and accuracy in work or energy calculations.

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