Thermodynamics part II.

Transcription

1 Thermodynamics part II. a.) Fenomenological thermodynamics macroscopic description b.) Molecular thermodynamics microscopic description b1.) kinetical gas theory b2.) statistical thermodynamics

2 Measuring temperatures - thermometers

3 Thermometers 1. Liquid thermometers Based on the linear expansion of the fluids Examples: alcoholic or mercury (Hg) thermometers

4 Thermometers 2. Gas thermometers Besed on the volume expansion at fixed pressure Examples:

5 Thermometers 3. Solid state thermometers Linear expansion of solids Examples: Bymetall Resistance thermometers pyrometers

6 Equation of ideal gases

7 Status indicators of ideal gases Pressure p dimension: Pa, pascals Volume V dimension: m 3 Absolute temperatue T dimension: K, kelvins

8 Status functions of ideal gases These are status indicators, if they are functions of other two status indicators, such as: p = p V, T V = V p, T T = T p, V

9 Ideal gas Definition: An ideal gas is a theoretical gas or gas model composed of a set of randomly moving, noninteracting (except elastical collisions between the point particles!!) point particles. We take into account the elastical collisions between the idealized particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

10 Combined gas law

11 Combined gas law general gas law Let us imagine the gas in its one state: n, p 1, V 1, T 1 status indicators of the given state: p 1, V 1, T 1 Keep the number of moles of the gas fixed and take the gas in a new state. In this new state the status indicators are: p 2, V 2, T 2 n, p 2, V 2, T 2 After many experiments have been made, the following rule has been decided: For the process (change of the state): p 1 V 1 = p 2 V 2 T 1 T 2

12 Ideal gas law

13 Ideal gas low equation of ideal gases n: number of moles or amount of substances p V ~n p V~T p V ~ n T p V = n R T R = J mol K universal gas constant

14 Other forms of the equation of ideal gases n = m M, M: molar mass g p V = n R T, kg, m: mass g, kg mol kmol p V = m M R T R p V = m M R T = m R M T = m R i T M = R i: individual gas constant

15 Special processes of ideal gases

16 Boyle Mariotte`s law = Boyle`s law Theorem: Keeping the temperature fixed, product of the pressure and the volume of the ideal gases is constant. p 1 V 1 = p 2 V 2 p V = constant

17 Gay-Lussac`s I. law Charles`s law Theorem: Keeping the pressure fixed, ratio of the volume and the temperature of the ideal gases is constant. V 1 T 1 = V 2 T 2 V T = constant

18 Gay-Lussac`s II. law = Gay-Lussac`s law Theorem: Keeping the volume fixed, ratio of the pressure and the temperature of the ideal gases is constant. p 1 T 1 = p 2 T 2 p T = constant

19 Heat, Specific heat, Molar heat = Molar heat capacity Heat capacity = Thermal capacity

20 Heat Joseph Black ( ) Experiments and observations on heat processes: For example: piece of iron and water in pan on the same oven surface, same time iron was very hot, water was just warm there are differences in heat at different materials Same heat can produce different change in temperature at different materials Heat has a quantity contacting bodies: Heat flows from one side to the other side T 1 HEAT T 2 T 1 > T 2

21 Heat After many observations: As consequence: Q ~ T Q ~ m Q ~ T m In order to solve the proportionality a new constant can be introduced: Q = c m T c = Q m T c: specific heat, c = J kg

22 Specific heats for ideal gases There are two types of specific heats for ideal gases: 1. Specific heat on constant volume = constant volume specific heat: c V 2. Specific heat at constant pressure = constant pressure specific heat: c p Connection bewteen the two types of specific heats: c p c V = R M

23 Specific heats for ideal gases c p c V = R M = R i Definitions: c p M c V M = R 1. Constant volume molar heat (molar heat capacity at constant volume): C V = c V M 2. Constant pressure molar heat (molar heat capacity at constant pressure): C p = c p M C p C V = R C p = C V = J kmol

24 Molar heats for ideal gases Types of the gases Single atomic gases (He, Ne, Ar, Kr, Xe, Rd, ) Double atomic gases (H 2, O 2, N 2, ) Gases with many atoms (CH 4, ) Constant volume molar heat capacity C V = 3 2 R C V = 5 2 R C V = 7 2 R Constant pressure molar heat capacity C p = 5 2 R C p = 7 2 R C p = 9 2 R

25 Heat capacity = Thermal capacity Definition: Heat capacity, or thermal capacity, is the measurable physical quantity that specifies the amount of heat energy required to change the temperature of an object or body by a given amount. The SI unit of heat capacity is joule per kelvin, J K = J Q = c m T K = Q T = c m K = J = J K