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PP207_Temperature

PP207_Temperature - Thermal Physics Temperature RHJansen...

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Unformatted text preview: Thermal Physics Temperature RHJansen Temperature A relative measure of how hot or cold something is. A scale is decided upon and how hot or cold various objects are is compared using the scale. Units Temperature T is measured in Kelvin K Change in Temperature T is measured in either Kelvin K or o Degrees Celsius C A change of 1 degree in Kelvin or Celsius is identical, so either unit can be used for a change in temperature. However, when a formula calls for the exact temperature we need to use the absolute temperature given by the Kelvin scale. RHJansen Converting Units Degrees Celsius + 273 = Kelvin Example 1 Convert 25oC to degrees Kelvin 25oC + 273 = 298oC RHJansen Speed and Temperature The temperature of a gas is related to the velocity of the gas particles. However, gas particles are in constant random motion. The particles are small and the space between them is large. They move with different speeds in different directions. They follow the Physics learned in mechanics, colliding with each other and the walls of their container creating pressure. As a result, only the average velocity can be calculated. However, if direction is included then the average would be zero. All the particles are moving in different directions, and every particle would be cancelled by another that is doing the opposite. If the velocities are squared then the plusses and minuses that indicate direction would be eliminated, but the magnitude would be squared. The average (mean) calculated needs to be square rooted to undo the affect of squaring everything. RHJansen Root Mean Squared Velocity The information on the proceeding slide leads to an equation relating gas speed to temperature. vrms Root Mean Squared Velocity R Universal Gas Constant (R = 8.31) kb Boltzman Constant (kb = 1.38 10-23) T M Temperature in Kelvin Molar mass (kg/mol) Mass of one mole of gas. Divide the mass number (grams/mole) by 1000 to convert kilograms/mole. vrms = 3 = 3 Molecular mass (kg/atom) Mass of one molecule of gas. Multiply the mass number (amu's) by the conversion to kilograms (1.6610-27 kg/amu) RHJansen Example 2 A gas at 25oC has a mass number of 10. a. Determine its molar mass in kg/mol. g 1 kg kg 10 = 0.010 mol 1000 g mol b. Determine the root mean squared velocity of the gas. rms = rms = 3RT M 3(8.31)(298) = 862 m s (0.010) RHJansen Example 3 A gas at 25oC has a mass number of 10. a. Determine the molecular mass in kilograms 1.66 10 - 27 kg 10 amu = 1.66 10 - 26 kg 1 amu b. Determine the root mean squared velocity of the gas. rms = rms = 3kb T m 3(1.38 10 - 23 )(298) = 862 m s - 26 (1.66 10 ) RHJansen Kinetic Energy of a Gas If gas particles have velocity, then they have kinetic energy. Kinetic energy is not a vector, and direction of motion does not matter. If it moves it has kinetic energy. 3 K = kb T 2 Example 4 Determine the average kinetic energy of a gas at 25oC. 3 K = kb T 2 3 K = (1.38 10 - 23 )(298) = 6.17 10 - 21 J 2 RHJansen Trends rms = Example 5 3RT = M 3kb T m 3 K = kb T 2 If the temperature of a gas doubles a. the speed of the molecules increase/decreases by a factor of... Increases by a factor of root 2 b. kinetic energy of molecules increase/decreases by a factor of... Increase by a factor of 2 As temperature increases the molecules move faster and as a result gain kinetic energy. RHJansen ...
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