Chapters 12 & 13 & 14

Thermodynamics

The Gas Laws

Boyle's Law

Keeping the temperature constant, the volume of a gas varies inversely with the absolute pressure.

(3)

Charles's Law

When the pressure is kept constant, the volume of a given amount of any gas varies directly with the thermodynamic temperature.

(4)

Gay-Lussac's Law

When the volume is kept constant, the absolute pressure of a given amount of any gas varies directly with the thermodynamic temperature.

(5)

Ideal Gas Law

(6)

Where and n is the number of moles.

or

(7)

Where N is the number of molecules and the Boltzmann's Constant is .

Example 6

A person's lungs might hold 6.0 L of air at body temperature (310 K) and atmospheric pressure (101 kPa). Given that the air is 21% oxygen, find the number of oxygen molecules in the lungs.

Solution:

Solve the ideal gas law for the number of molecules:

Then find 21% of this number:

Example 7

Feeling a bit cool, you turn up the thermostat in your house or apartment. A short time later the air is warmer. Assuming the room is well sealed, is the pressure of the air (a) greater than, (b) less than, or (c) the same as before you turned up the heat?

Solution:

(a) The air pressure increases.

Example 8

A cylindrical flask of cross-sectional area A is fitted with an airtight piston that is free to slide up and down. Contained within the flask is an ideal gas. Initially the pressure applied by the piston is 130 kPa and the height of the piston above the base of the flask is 25 cm. When additional mass is added to the piston, the pressure increases to 170 kPa. Assuming the system is always at the temperature 290 K, find the new height of the piston.

Solution:

Example 9

Consider again the system in the previous example. In this case the temperature is changed from an initial value of 290 K to a final value of 330 K. The pressure exerted on the gas remains constant at 130 kPa, and the initial height of the piston is 25 cm. Find the final height of the piston.

Solution:

Example 10

A cylinder contains 12 L of oxygen at 20°C and 15 atm. The temperature is raised to 35°C, and the volume is reduced to 8.5 L. What is the final pressure of the gas in atmospheres? Assume that the gas is ideal.

Solution:

Write the initial and final states using the ideal gas law:

Divide the final by the initial and solve for the final pressure:

Substitute the numerical values:

The Kinetic Theory:

The temperature of an ideal gas is proportional to the average translational kinetic energy of its molecules.

(8)

Speed of Molecules in a Gas

(9)

Example 11

Find the average kinetic energy of oxygen molecules in the air. Assume the air is at a temperature of 21°C.

Solution:

Example 12

The atmosphere is composed primarily of nitrogen (78%) and oxygen (21%). (a) Is the rms speed of (28.0 g/mol) greater than, less than , or the same as the rms speed of (32.0 g/mol)? (b) Find the rms speed of and at 293 K.

Solution:

(a) rms for nitrogen is greater because it has less mass.

(b)

On to the Mechanical Equivalent of Heat