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Chapter 20: Problem 20

Is it a violation of the Second Law of Thermodynamics to capture all the exhaust heat from a steam engine and funnel it back into the system to do work? Why or why not?

Short Answer

Expert verified
Answer: Yes, it is a violation of the Second Law of Thermodynamics to capture all the exhaust heat from a steam engine and funnel it back into the system to do work. This would imply a total conversion of heat into work with no increase in entropy, which is not possible according to the Second Law. There will always be some loss of energy in the form of waste heat that cannot be converted into work, making 100% heat engine efficiency unattainable.

Step by step solution

01

Understand the Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time; it can only remain constant or increase. In other words, natural processes tend to move towards a state of greater disorder (entropy). This means that it is impossible to convert heat completely into work without any increase in entropy.
02

Analyze the steam engine system

A steam engine operates initially by adding heat to water to generate steam. Next, the steam is used to perform work (e.g., turning a wheel or piston). After performing work, the steam's temperature drops, and it then needs to be cooled down to form water again before being reused.
03

Consider the heat recovery process

If we were to capture all the exhaust heat from the steam engine and funnel it back into the system, we would essentially be trying to create a 100% efficient heat engine. This would mean converting all the heat from the steam back into work without losing any energy in the form of waste heat.
04

Apply the Second Law of Thermodynamics to this scenario

According to the Second Law of Thermodynamics, it is impossible to convert heat completely into work with no increase in entropy. The attempt to capture all exhaust heat implies that no entropy increase would occur, but this contradicts the Second Law.
05

Determine if this is a violation of the Second Law of Thermodynamics

Yes, it is a violation of the Second Law of Thermodynamics to capture all the exhaust heat from a steam engine and funnel it back into the system to do work. Such a process would imply total conversion of heat into work with no increase in entropy, which is not possible according to the Second Law of Thermodynamics. There will always be some loss of energy in the form of waste heat that cannot be converted into work, which explains why 100% heat engine efficiency is unattainable.

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Most popular questions from this chapter

Consider a system consisting of rolling a six-sided die. What happens to the entropy of the system if an additional die is added? Does it double? What happens to the entropy if the number of dice is three?

Suppose an atom of volume \(V_{\mathrm{A}}\) is inside a container of volume \(V\). The atom can occupy any position within this volume. For this simple model, the number of states available to the atom is given by \(V / V_{A}\). Now suppose the same atom is inside a container of volume \(2 V .\) What will be the change in entropy?

An outboard motor for a boat is cooled by lake water at \(15.0^{\circ} \mathrm{C}\) and has a compression ratio of \(10.0 .\) Assume that the air is a diatomic gas. a) Calculate the efficiency of the engine's Otto cycle. b) Using your answer to part (a) and the fact that the efficiency of the Carnot cycle is greater than that of the Otto cycle, estimate the maximum temperature of the engine.

A water-cooled engine produces \(1000 .\) W of power. Water enters the engine block at \(15.0^{\circ} \mathrm{C}\) and exits at \(30.0^{\circ} \mathrm{C}\). The rate of water flow is \(100 . \mathrm{L} / \mathrm{h}\). What is the engine's efficiency?

An ideal gas is enclosed in a cylinder with a movable piston at the top. The walls of the cylinder are insulated, so no heat can enter or exit. The gas initially occupies volume \(V_{1}\) and has pressure \(p_{1}\) and temperature \(T_{1}\). The piston is then moved very rapidly to a volume of \(V_{2}=3 V_{1}\). The process happens so rapidly that the enclosed gas does not do any work. Find \(p_{2}, T_{2},\) and the change in entropy of the gas.
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