Thermodynamics Practice Problems & Solutions

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  • 0:05 What Is Entropy?
  • 1:07 Car Engines
  • 2:35 Engine Efficiency
  • 5:24 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

Heat energy flows from warmer objects to cooler objects. In this lesson, we will focus on entropy, which is the disorder of a system. We will also determine the efficiency of some heat engines that utilize temperature gradients to do work.

What Is Entropy?

Imagine the difference between the crumpled up clothes in the dirty laundry hamper, and the clean clothes neatly folded in the dresser drawers. It takes a lot less effort to let the clothes pile up in the dirty laundry hamper than it does to neatly fold them and put them away in their proper place. This is an example of the concept of entropy, which is the natural tendency for a system to become more disordered. Entropy is a thermodynamics concept that deals with the disorder and randomness of molecules.

Another example of an increase in entropy is putting an ice cube into a hot drink. Heat flows from the warmer liquid to the ice cube and melts the ice. Even though very little heat was added to the system (ice does contain some heat), the entropy of the system increased because solid water (ice) has a structured arrangement of its molecules. When it melts, the structure is gone and the molecules are randomly arranged, making the system more disordered.

Now that we have an understanding of entropy, let's focus on entropy in relation to heat engines.

Car Engines

Cars are almost an essential part of our daily lives. People that have to drive a lot might make a decision on which car to drive based on how well the car's engine can conserve gasoline. Unfortunately, a lot of the gasoline we buy to feed our car's engine only makes the engine hot. Let's see how a car engine turns gasoline into movement.

Inside the car engine are cylinders and pistons. The pistons are cylindrical pieces of metal that move up and down inside the cylinder. Attached to the bottom of the piston is a connecting rod, which is attached to the crankshaft. The crankshaft is connected to the flywheel, which turns the gears in the transmission when it's engaged. The transmission essentially turns the wheels and your car moves down the road. It's what happens inside of the cylinder that we need to focus on.

Gasoline and air are ignited inside the cylinder when the piston is at the top of the cylinder. When temperature increases, the disorder of the system increases, which is an increase in entropy. The exploding gas wants to expand in all directions, but the thick metal of the cylinder wall won't allow this. Only the molecules aimed at the piston push it downwards, ultimately causing the wheels of the car to move.

The energy of the molecules that don't cause the piston to move go into heating the cylinder. Some of the energy of the molecules that do strike the piston is lost to heat as well. This leads us directly into a discussion of the efficiency of the engine.

Engine Efficiency

The heat engine we have been discussing works on the flow of heat energy. A temperature gradient is a difference in temperature between two separate locations. Imagine the temperature difference between the temperature inside the cylinder when the engine is running versus the temperature of the exhaust. The exhaust is warm, but the temperature inside the cylinder is blistering. Heat coming out as exhaust is lost energy. Let's look at this diagram on your screen that's showing the conceptual flow of heat in a heat engine.

Diagram 1. Heat flows from high to low temperatures doing some work.

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