**Charles’ Law**

# The Temperature-Volume Relationship

**Charles’ Law**

# French chemist **Jacques Charles** discovered that the volume of a gas at constant pressure changes with temperature.

# As the temperature of the gas increases, so does its volume, and as its temperature decreases, so does its volume.

**C h a r l e s ’ L a w**

# The law says that at constant pressure, the volume of a fixed number of particles of gas is directly proportional to the absolute (Kelvin) temperature, mathematically expressed as:

**V = ***k***T**

**Charles’ Law**

**V = ***k***T**

# V = Volume

* k *= Charles’ Law constant of Proportionality

# T = Temperature in Kelvins

**Explanation**

# Raising the temperature of a gas causes the gas to fill a greater volume as long as pressure remains constant.

# Gases expand at a constant rate as temperature increases, and the rate of expansion is similar for all gases.

**Example**

# If the temperature of a given amount of gas is doubled, for example, its volume will also double (as long as pressure remains unchanged).

**2V = 2***k***T**

**Charles’ Law**

# Charles’ Law can be modified to a convenient form by solving for *k*.

*k ***= V / T**

**Charles’ Law**

# In a sample with volume V1 & temperature T1, changing either volume or temperature converts these variables to V2 and T2.

**V****1**** / T****1 ****= ***k = ***V****2 ****/ T****2**

# Therefore:

**V****1**** T****2 ****= V****2**** T****1**

**Demonstration of Charles’ Law**

**Relationship of Boyle’s Law and Charles’ Law**

**Practical Applications**

…

# Charles’ Law

# By Raymond Greenlaw

# Learning Objectives

# State Charles’ Law

# Understand Charles’ Law

# Apply Charles’ Law

# Explain relevance of Charles’ Law to scuba

# Jacques Charles/Joseph Louis Guy-Lussac

# Ballooner and scientist

# 1787

# Did not publish, sometimes called Charles/Guy-Lussac’s Law after Joseph Louis Guy-Lussac

# Temperature Scales

# State Charles’ Law

# For any gas at a constant pressure, the volume of the gas is directly proportional to its absolute temperature.

# State Charles’ Law

# Mathematically,

# V1/T1 = V2/T2, where Vi is volume and Ti is temperature in Kelvin

# V/T = k, where k is a constant

# Recall 0K = -273C and oK = -460F

# Note, pressure remains the same

# Charles’ Law Illustrated

# Understand Charles’ Law

# Temperature goes up volume goes up

# Temperature goes down volume goes down

# Rubber glove thought experiment

# Gas molecules thought experiment

# Balloon in the morning thought experiment

# Example

# 2 liters of gas at 273C

# 1 liter of gas at oC

# Since V1/T1 = V2/T2, we have 2/546 = 1/273

# Note, we converted temperatures to Kelvin by adding 273 as required by Charles’ Law.

# If we cool by 273C, we reduce volume by 1 liter.

# If we heat by 273, we increase volume by 1 liter.

# Apply Charles’ Law

# Not fully (XL) BCD contains .3 liters of air on a cool morning at oC

# BCD is left in a car and the temperature sores to 40C

# What is the new volume of air in the BCD, assuming it is still not totally full?

# Apply Charles’ Law (We assume no change in pressure.)

# We know intuitively that the volume goes up.

# .3/273 = x/313, so x = .34 liters

# Explain Relevance of Charles’ Law to Scuba

# We learned that as temperature increases volume increases.

# Consider a full cylinder of air.

# When heated the volume wants to increase by Charles’ Law, but in a tank there is no room for expansion, so the pressure must increase.

# Extreme temperature increases could result in a tank bursting.

# Do not leave full scuba tanks stored in direct sunlight or heat them.

# Getting Bent

# We know nitrogen dissolves in a diver’s body tissues under pressure.

# Suppose a diver goes deep and a lot of nitrogen dissolves in body tissues.

# As the diver surfaces, the diver is not bent.

# However, exposure to intense sunlight could cause gas coming out of solution to increase in volume (temperature goes up volume increases), so the diver could get bent.

# Question

# What happens if we fill tanks on a hot afternoon and dive the next day on a very cold morning?

# References

# Naui Master Scuba Diver Manual, 2010.

# answers.yahoo.com

# www.thescubaguide.com

# www.wikianswers.com/Q/What_is_Boyle’s_law_in_regards_to_scuba_diving

# Figures borrowed from around the web, please let me know if any of the figures are not in the public domain and I will replace them.

# Questions

# Thanks for coming!

# www.raymondgreenlaw.com

…