# AP Physics Chapter 11 Study Guide

## Using Energy

### Example 1

A 20% efficient engine accelerates a 1500 kg car from rest to 15 m/s. How much energy is transferred to the engine by burning gasoline?

### Getting Energy from Food

1.00 calorie is equivalent to 4.19 joules

### Example 2

An "energy bar" contains 6.0 g of fat. How much energy is this in joules? In calories? in Calories?

### Example 3

Suppose your body was able to use the chemical energy in gasoline. How far could you pedal a bicycle at 15 km/hr on the energy of 1 gallon of gas? (1 gallon of gas has a mass of 3.2 kg.)

## Thermal Energy and Temperature

### An atomic view of thermal energy and temperature

Ideal Gas - A hypothetical gas whose molecules bounce off each other (and the boundaries of their container) with perfect elasticity and have negligible size, and in which the intermolecular forces acting between molecules not in contact with each other are also negligible.

The thermal energy of an ideal gas is equal to the total kinetic energy of the atoms that make up the gas.

The temperature of an ideal gas is a measure of the average kinetic energy of the atoms that make up the gas.

Meaning of Temperature on the Kelvin Scale

Zero on the Kelvin scale is the point at which the kinetic energy is zero.

T = TC + 273

Boltsmann's Constant

kB = 1.38 x 10-23 J/K

rms speed and temperature

Thermal Energy is directly proportional to temperature

### Example 4

What are the rms speeds of helium and argon in a gas at 1000˚C?

### Example 5

At what temperature do hydrogen molecules have the same rms speed as nitrogen molecules at 100˚C?

### Heat and the First Law of Thermodynamics

Heat and work are two different ways of transferring energy to or from a system.

Heat is the energy transfer during a thermal interaction.

### An Atomic Model of Heat

Thermal energy is transferred from the faster moving atoms on the warmer side to the slower moving atoms on the cooler side.

Thermal Equilibrium - two systems placed in thermal contact will transfer thermal energy until their final temperatures are the same.

Heat is transferred from hot to cold.

### Example 6

600 J of heat energy are transferred to a system that does 400 J of work. By how much does the system's thermal energy change?

### Example 7

10 J of heat are removed from a gas sample while it is being compressed by a piston that does 20 J of work. What is the change in the thermal energy of the gas? Does the temperature of the gas increase or decrease?

### Heat Engines

A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. The mechanical output is called work, and the thermal energy input is called heat.

### Example 8

A heat engine does 20 J of work while exahusting 30 J of waste heat. What is the engine's efficiency?

### Example 9

A heat engine with an efficiency of 40% does 100 J of work. How much heat is
(a) extracted from the hot reservoir and

(b) exhausted into the cold reservoir?

### Heat Pumps

A heat pump is a machine or device that moves heat from one location (the 'source') to another location (the 'sink' or 'heat sink') using mechanical work.

Coefficient of Performance (COP) is analogous to efficiency

Theoretical maximum COP of a heat pump used for cooling

Theoretical maximum COP of a heat pump used for heating

### Example 10

Find the maximum possible coefficient of performance for a heat pump used to heat a house in a northerly climate in winter. The inside is kept at 20˚C while the outside is -20˚C.

### Entropy and the Second Law of Thermodynamics

Irreversible process - An irreversible process is one in which the intermediate states cannot be specified by any set of macroscopic variables and which are not equilibrium states. Since the intermediate states are unknown this process cannot be reversed.

or

An irreversible process is a process that cannot return both the system and the surroundings to their original conditions. That is, the system and the surroundings would not return to their original conditions if the process was reversed.

Entropy - A measure of the disorder or randomness in a closed system.

Entropy increases as two systems with initially different temperatures move towards thermal equilibrium.

Second Law of Thermodynamics - The entropy of an isolated system never decreases. The entropy either increases, until the system reaches equilibrium, or, if the system began in equilibrium, stays the same.

When another form of energy is converted to thermal energy, there is an increase in entropy. The process will not spontaneously reverse.