Carnot cycle derivation pdf

Carnot cycle derivation pdf

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It’s the shape of the curve that’s important.] The gas traverses the cycle in a The most important result of the Carnot cycle is the derivation of the Carnot theorem, which states “No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between those same reservoirs.”1 In other words, Carnot Cycle efficiency is the maximum efficiency achieved for any cycle that operates Figureshows this cycle which consists of an CARNOT CYCLES. (Historical Note: actually, Carnot thought at the time that heat was a fluid Figure shows the schematic and accompanying P-v diagram of a Carnot cycle executed by water steadily circulating through a simple vapor power plant. Proof of Clausius-Clapeyron using Gibbs Function or Gibbs Free Energy For any two phases The Carnot cycle is quite relevant to atmospheric science because the atmosphere can be thought of as a Carnot cycle where solar energy (heat is absorbed) and IR energy is expelled and some fraction of the absorbed energy is used to drive atmospheric circulation (which is the mechanical work) against frictional forces Carnot cycle. For a typical steam power plant operating between T H= K Not surprisingly, perhaps, Carnot visualized the heat engine as a kind of water wheel in which heat (the “fluid”) dropped from a high temperature to a low temperature, losing “potential energy” which the engine turned into work done, just like a water wheel. Sadi Carnot was a French physicist who proposed an “ideal” cycle for a heat engine in Historical note – the idea of an ideal cycle came about because Carnot cycle is a thermodynamic process that undergoes four important steps of either gas expansion or compression under particular conditions that ultimately lead to production PVdiagram is called the Carnot cycle. The idea is to minimize the entropy generated at each stage. The Thermal Efficiency of the Carnot cycle is derived above and the StepDerive the parent expression for the state property of interest: Eg. dU = dq + dw = TdS PdV. StepExpress the same differential using the chain rule of partial differentiation: dU U dS U dV. The Carnot Cycle. If the gas absorbs an amount Q hfrom the hot reservoir, the entropy of the The Carnot cycle when acting as a heat engine consists of the following steps: (Reversible) isothermal expansion of the gas at the hot temperature, T1 = TH (isothermal heat Carnot’s theorem: A reversible engine operating between anygiven reservoirs (i.e., Carnot engine) is the most efficient that can operate between those reservoirs. Therefore, the Carnot heat engine defines the maximum efficiency any practical heat engine can reach up to. All standard heat engines (steam, gasoline, diesel) work by supplying heat to The p-V diagram below sketches the operation of a Carnot engine, where the \working uid that expands and contracts within the cylinder is an ideal gas. Thermal efficiency η th=W net/Q H=1-(Q L/Q H)=f(T L,T H) and it can be shown that η th=1-(Q L/Q H)=1-(T L/T H). This is called the Carnot efficiency. Michael Fowler. FigCarnot vapor cycleThe steam exiting the boiler expands adiabatically through the turbine and work is developed The work done in the cycle is equal to the area enclosed on a p V diagram. (No The Carnot Cycle derivation was presented below in a written format. The Ultimate in Fuel Efficiency. Consider the following reversible cyclic process involving one mole of an ideal gas: Isothermal expansion from (P1,V1,Th) to (P2,V2,Th), FigAdiabatic Carnot Efficiency. Therefore dw= (v l)de s (3) Also, q h = l v, therefore, l v T = (v l)de s dT (4) Which can be re-written as de s dT = l v T(v l) (5) Which is the Clausius-Clapeyron Equation 1a. P= NkT V (2) while an adiabatic curve obeys P= K V (3) where Kis a constant and =(f+2)=fwhere fis the number of degrees of freedom of each molecule. = S V + V S. StepEquate terms containing the same differential between these two equations to get statement). V pT L T H a b c d The Carnot cycle Carnot proposed a cycle which would give the maximum possible efficiency between temperature limits. Applet here! For a monatomic ideal gas, =A Carnot cycle is shown in Fig[The units are arbitrary. Carnot heat engine operating between a high-temperature source at K and reject heat to a low-temperature reservoir at K. (a) Determine the thermal Tags Heat Engines: the Carnot Cycle. Thermal Efficiency = Workdone/Amount of heat supplied. Work done (W) = Heat supplied (Qs)-Heat rejected (QR) Now project the values into the equation and get the thermal efficiency which is shown below.