in the context of thermodynamics how do theoretical models of entropy and enthalpy changes in cl

In the context of thermodynamics how do theoretical models...

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The concept of entropy and the second law of thermodynamics was first developed by a French engineer named Sadi Carnot in the $1820 \mathrm{~s}$ in a study of the efficiency of the newly developed steam engines and other types of heat engines. Basically, a steam engine works in a cyclic manner; in each cycle, it withdraws energy as heat from some high-temperature thermal reservoir, uses some of this energy to do work, and then discharges the rest of the energy as heat to a lower-temperature thermal reservoir. The maximum amount of work will be obtained if the cyclic process is carried out reversibly. Of course, the maximum amount of work cannot be achieved in practice because the reversible process is idealized, but the results give us a measure of the maximum efficiency that can be expected. Because the process is cyclic and reversible, we have $\Delta U_{\text {engine }}=q_{\mathrm{rev}, \mathrm{h}}-q_{\mathrm{rev}, \mathrm{c}}-w=0$ where $q_{\mathrm{rev}, \mathrm{h}}$ is the energy withdrawn reversibly as heat from the high-temperature reservoir at temperature $T_{\mathrm{h}}, q_{\mathrm{rev}, c}$ is the energy discharged reversibly as heat to the lower-temperature reservoir at temperature $T_{c}$, and $w$ is the work performed. Defining the efficiency of such an engine as the ratio of the work performed by the engine to the amount of heat extracted from the high-temperature reservoir, $w / q_{\mathrm{h}}$, use the above equation and Equation $23.1$ to show that the efficiency of such an engine is given by $$ \text { efficiency }=\frac{w}{q_{\mathrm{h}}}<\frac{T_{\mathrm{h}}-T_{\mathrm{c}}}{T_{\mathrm{h}}} $$ Calculate the maximum efficiency of a steam engine that extracts energy in the form of heat from boiling water at $100^{\circ} \mathrm{C}$ and releases it into its surroundings at $20^{\circ} \mathrm{C}$. Under what conditions would this engine achieve $100 \%$ efficiency?

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3. A simple heat engine. Suppose you have two rooms: A hot one whose temperature is maintained equal to T1 and a cold one with the temperature T2. You can construct a cyclically operating heat engine that extracts heat from the hot room and uses it to perform mechanical work. We will use 1 mol of an ideal gas to perform work and the cycle of our engine will consist of four steps: Step 1: While in the 1st room, the gas expands reversibly at constant temperature T1 thereby performing positive work that can be used, e.g., to lift a weight. The initial volume of the gas is V1 and the final volume V2. Step 2: The container with the gas is transferred to the 2nd room, where the gas is allowed to cool down at constant volume (V2) until it attains the room temperature T2. Step 3: The gas is compressed reversibly from V2 to V1 at constant temperature T2. Step 4: The gas is transferred back to the 1st room where it is allowed to equilibrate with the room until it reaches the room temperature T1. The volume is kept constant during this step. At the end of Step 4 the gas returns to its original state. We will assume that transferring the container between the two rooms can be done at no cost (no work necessary). The heat capacity of the gas is temperature independent and equal to Cv. A. What is the total work W done by the gas during the cycle? B. The efficiency ̗ of a heat engine can be defined as the ratio of the work W and the total heat received by the gas from the hot room (i.e., the heat q = q1 + q4 absorbed by the gas during Steps 1 and 4). What is the efficiency of this engine? What is the maximum possible efficiency of such an engine (with given T1 and T2)? C. What is the change of the entropy of the gas as a result of the cycle? D. What is the change of the entropy of the Universe as a result of the cycle? (For the purposes of this problem the Universe consists of the two rooms and the gas). E. Is it possible to build a more efficient heat engine than the one described here? In other words, do you think some of the heat from the hot room is "wasted", and if so, at what steps of the cycle is it wasted? How could one modify these steps to improve efficiency?

Dominador T.

Transcript

00:01 So assuming the process to be refusable, we have the entropy change in the engine being equal to delta s -h plus delta s -c, which is equal to q -h divided by t -h minus qc divided by t -c.

00:24 So we know that the internal energy change in the engine is equal to q -h minus qc -c -minors, which work being equal to 0.

00:36 What this means is work is equal to qh minus qc.

00:42 So let's just write these equations with equation one and we've got equation two.

00:48 So looking at these two equations from equation one, what we have here is qc over th being equal to qh over tc.

01:00 So looking at this, we can also write this as qc being equal to qh multiplied by tc over t .h...

Question

.In the context of thermodynamics, how do theoretical models of entropy and enthalpy changes in closed systems inform the design of heat engines, with a focus on optimizing efficiency while minimizing energy losses and environmental effects?

Question

.In the context of thermodynamics, how do theoretical models of entropy and enthalpy changes in closed systems inform the design of heat engines, with a focus on optimizing efficiency while minimizing energy losses and environmental effects?

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