Charles’ Law Volume & temperature

Temperature Changes & Matter Solids & Liquids expand/contract as temperature changes usually very small change Gases show large volume changes with temperature changes

balloons can expand & contract with Δ temp

Jacques Charles Balloonist 1787: experiments that showed how volume of gases depends on temperature

How do hot air balloons work?

Relationship between V and T Pressure & # moles are held constant At high temp, gas particles move faster and collide with walls more often Pressure is constant, so volume will increase

Data for Volume-Temperature 202 300 5 167 200 4 132 100 3 114 50 2 10 1 Volume (mL) Temperature (C) Trial

What did Charles do next? Graph results

volume vs temperature

Linear Relationship Plot Volume vs ˚C : forms straight line relationship between V and T is linear

Charles extrapolated graph to 0 volume and found X-intercept is -273 ˚C

Hints of Kelvin scale Charles extrapolated data to see T at which volume was 0ml first indication that T of -273 ˚C had fundamental meaning Why did Charles have to extrapolate his lines in this temperature range instead of collecting data? -273 ˚C

Plot Volume vs. T (K) Get straight line passing through 0 point relationship between V & T is direct

The low temperature region is always extrapolated. Why?

Charles’ Law: Verbal volume of gas at constant pressure varies directly with its absolute temperature

Charles’ Law: Graphically Plot V vs Kelvin T Straight line passing through 0 V = kT or V = k T

Charles’ Law: Mathematically V = k T V1 = V2 Given any 3 variables, can find 4th

Problem 1 150 mL of a gas at constant pressure Temperature increases from 20˚C to 40˚C What is the new volume?

Step 1: Convert T1 and T2 to Kelvin Step 2: Rearrange equation: V1 = V2 becomes V1T2 = V2 T1 T2 T1 Step 3: Substitute and solve: (150 mL)(313 K) = 160 mL 293 K