NJC Temperature and Ideal Gas notes

National Junior College Science Department | Physics 1 12. Temperature & Ideal Gases Content Page 12.1 Temperature Scales ................................ ................................ ................................ ............3 12.1.1 Absolute scale of temperature ................................ ................................ .................3 Exercise 1: Thermal Equilibrium and Temperature Scale ................................ ........................4 12.2 Equation of State ................................ ................................ ................................ .............5 12.2.1 Concept of the Mole ................................ ................................ ................................ .5 12.2.2 Equation of State ................................ ................................ ................................ .....6 Exercise 2: Equation of State ................................ ................................ ................................ ..8 12.3 Kinetic theory of gases ................................ ................................ ................................ ........9 12.3.1 Assumptions of kinetic theory of gases ................................ ................................ ....9 Exercise 3: Kinetic Theory of Gases ................................ ................................ ......................16 12.4 Kinetic Energy of a Molecule ................................ ................................ .........................17 Exercise 4: Kinetic Energy of a Molecule ................................ ................................ ...............18

National Junior College Science Department | Physics 2 Learning Objectives 12.1 Temperature Scales (a) Show an understanding that a thermodynamic scale of temperature has an absolute zero and is independent of the property of any particular substance. (b) Convert temperatures measured in degrees Celsius to kelvin: ܶ/ܭ= ߠ/°ܥ+ 273.15. 12.2 Equation of State (c) Recall and use the equation of state for an ideal gas expressed as ܸ݌= ܶ݇ܰwhere ܰ is the number of particles. (d) State that one mole of any substance contains 6.02 × 10ଶଷ particles, and use the Avogadro constant ܰ஺ = 6.02 × 10ଶଷ mol−1 as well as the relationship ݇ܰ= ܴ݊ between the Boltzmann constant and the molar gas constant (݊ is the amount of substance in moles). 12.3 Kinetic theory of gases (e) State the basic assumptions of the kinetic theory of gases. (f) Explain how the random motion of gas particles exerts mechanical pressure and hence derive, using the definition of pressure as force per unit area, the relationship , ܸ݌= ଵ ଷ݉ܰ⟨ܿଶ⟩ (a simple model considering one -dimensional collisions and then extending to three dimensions using ⟨ܿ௫ଶ⟩ = ଵ ଷ ⟨ܿଶ⟩ is sufficient). 12.4 Kinetic energy of a molecule (g) Recall and use the relationship that the mean translational kinetic energy of a particle of an ideal gas is (directly) proportional to the thermodynamic temperature (i.e. ଵ ଶ݉⟨ܿଶ⟩ = ଷ ଶܶ݇ )to solve problems.

National Junior College Science Department | Physics 3 12.1 TEMPERATURE SCALES 12.1.1 Absolute scale of temperature (a) Show an understanding that a thermodynamic scale of temperature has an absolute zero and is independent of the property of any particular substance. (b) Convert temperatures measured in degrees Celsius to kelvin: ܶ/ܭ= ߠ/°ܥ+ 273.15. The thermodynamic scale is based on the idea that the average kinetic energy of a gas molecule is proportional to the thermodynamic temperature, and it is the same for all substances at a particular thermodynamic temperature . Therefore, the temperature scale is independent of the property of the substance. We say that the thermodynamic temperature scale is an absolute scale. An absolute temperature scale is not defined in terms of a property of any particular substance. The thermodynamic scale has two fixed points:  an absolute zero, which is defined as zero kelvin or 0 K Absolute zero is the temperature at which all substances have the minimum internal energy1.  triple point of water2, the temperature at which ice, water and water vapour can co-exist, which is defined as 273.16 K (equal to 0.01 °C). The gap between absolute zero and the triple point of water is divided into 273.16 equal divisions. Each division is 1 K. The scale is defined so that the scale divisions on the thermodynamic scale are equal in size to the divisions on the Celsius scale. The temperature in Celsius is defined as the temperature in Kelvin minus 273.15 so T / K = T / °C + 273.15 (e.g. pure water freezes at 273.15 K or 0 oC and boils at 373.15 K or 100 oC at standard atmospheric pressure, the difference is both 100 units.) Self-study resources Video explanation of the absolute zero temperature. youtu.be/iMrWN99XHvQ 1 In classical physics, the internal energy of a substance is zero at absolute zero. In quantum physics, it is impossible for any molecule or atom to be stationary due to Heisenberg Uncertainty Principle. Hence , absolute zero is defined as the temperature for which substances have the lowest internal energy. 2 In thermodynamics, the triple point of a substance is the temperature and pressure at which the thre e phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. Recall & apply in problems You need to explain this You need to explain this

National Junior College Science Department | Physics 4 Exercise 1: Thermal Equilibrium and Temperature Scale You should take about 15 minutes to complete this exercise. 1.1 A student draws a linear graph on the axes shown in order to convert temperatures in Kelvin to temperatures in degrees Celsius. What is the intercept on the vertical axis and the gradient of the line? (2005 P1 Q13) 1.2 (a) State (i) in what way the absolute scale of temperature differs from other temperature scales, [1] (ii) what is meant by the absolute zero of temperature. [1] (b) The temperature of a water bath increases from 50.00°C to 80.00°C. Determine, in kelvin and to an appropriate number of significant figures, (i) the temperature 50.00°C, [1] (ii) the change in temperature of the water bath. [1] Answer key 1.1 B 1.2 (b)(i) 323.15 K 1.2 (b)(ii) 30.00 K

National Junior College Science Department | Physics 5 12.2 EQUATION OF STATE (c) Recall and use the equation of state for an ideal gas expressed as pV = NkT, where N is the number of particles. (d) State that one mole of any substance contains 6.02 ×1023 particles and use the Avogadro constant NA = 6.02 × 1023 mol−1 as well as the relationship Nk = nR between the Boltzmann constant and the molar gas constant (n is the amount of substance in moles). 12.2.1 Concept of the Mole Self-study resources This video covers the term “mole”, explains “Avogadro number”, and runs through examples of the sort of calculations you might have to do with moles. youtu.be/wPGVQu3UXpw Amount of gas is measured in moles. One mole of any substance contains 6.02 × 1023 particles The Avogadro number NA is NA = 6.02 × 1023 mol–1 The number of moles n of a gas can be calculated by n = mass of substance molar mass of gas or n= number of gas molecules Avogadro number NA We can obtain the approximate molar mass of a substance if its mass number is known The molar mass of the substance is approximately equal to the mass number expressed in grammes For example: The mass number of iron–56 atom ( Fe26 56 ) is 56. So, the molar mass is ≈ 56 g. Recall & apply in problems Refer to “data and formulae” Rec