Thermodynamics. Joule-Thomson effect Ideal and Real Gases. What you need: Complete Equipment Set, Manual on CD-ROM included

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Ideal Real Gases Thermodynamics 30600 What you can learn about Real gas Intrinsic energy Gay-Lussac theory Throttling Van der Waals equation Van der Waals force Inverse Inversion temperature

are measured at various pressures the Joule-Thomson coefficients of the gases in question are calculated What you need: Joule-Thomson apparatus 0436100 1 Temperature meter digital, 4-1361793 1

1 Ideal Real Gases Thermodynamics What you can learn about Real gas Intrinsic energy Gay-Lussac theory Throttling Van der Waals equation Van der Waals force Inverse Inversion temperature Principle: A stream of gas is fed to a throttling point, where the gas (CO or N ) undergoes adiabatic expansion The differences in temperature established between the two sides of the throttle point are measured at various pressures the Joule-Thomson coefficients of the gases in question are calculated What you need: Joule-Thomson apparatus Temperature meter digital, Temperature probe, Pt Pressure-reducing valves, CO / He Pressure-reducing valves, nitrogen Wrench for steel cylinders Steel cylinder, nitrogen, 10 l Steel cylinder, CO, 10 l Gas-cylinder Trolley for Cylinder Hose clip for 1-0 diameter tube Rubber tubing, vacuum, id = 8 mm Complete Equipment Set, Manual on CD-ROM included P30600 Temperature differences measured at various ram pressures Tasks: 1 Determination of the Joule-Thomson coefficient of CO Determination of the Joule-Thomson coefficient of N PHYWE Systeme GmbH & Co KG D Göttingen Laboratory Experiments Physics 149

LEP 306 Related topics Real gas; intrinsic energy; Gay-Lussac theory; throttling; Van der Waals equation; Van der Waals force; inverse Joule- Thomson effect; inversion temperature Principle A stream

2 LEP 306 Related topics Real gas; intrinsic energy; Gay-Lussac theory; throttling; Van der Waals equation; Van der Waals force; inverse Joule- Thomson effect; inversion temperature Principle A stream of gas is fed to a throttling point, where the gas (CO or N ) undergoes adiabatic expansion The differences in temperature established between the two sides of the throttle point are measured at various pressures the Joule- Thomson coefficients of the gases in question are calculated Equipment Joule-Thomson apparatus Temperature meter digital, Temperature probe, immers type Reducing valve for CO / He Reducing valve f nitrogen Wrench for steel cylinders Steel cylinder rack, mobile Steel cylinder, CO, 10 l, full Steel cylinder, nitrogen, 10 l, full Tasks 1 Determination of the Joule-Thomson coefficient of CO Determination of the Joule-Thomson coefficient of N Set-up procedure The set-up of the experiment is as in Fig 1 If necessary, screw the reducing valves onto the steel cylinders check the tightness of the main valves Secure the steel cylinders in their location Attach the vacuum between the reducing valve the Joule-Thomson apparatus with hose tube clips On each side of the glass cylinder, introduce a temperature probe up to a few millimetres from the frit attach with the union nut Connect the temperature probe on the pressure side to inlet 1 the temperature probe on the unpressurised side to inlet of the temperature measurement apparatus Important: The experimenting room the experimental apparatus must be in a thermal equilibrium at the start of the measurement The experimental apparatus should be kept out of direct sunlight other sources of heating or cooling Fig 1: Experimental set-up: PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co KG D Göttingen P

3 LEP 306 Set the temperature measurement apparatus at temperature difference measurement Temperature meter should be switched on at least 30 min before performing the experiment to avoid thermal drift Read operating instructions for further explanations of the temperature meter Open the valves in the following order: steel cylinder valve, operating valve, reducing valve, so that an initial pressure of 100 k is established Reduce the pressure to zero in stages, in each case reading off the temperature difference one minute after the particular pressure has been established Perform the measurement for both gases, determine the atmospheric pressure ambient temperature Theory evaluation The state for real gases is given by the van der Waals equation a p a b 1V b RT V where p is the pressure, V the molar volume T the temperature of the gas R is the universal gas constant, a b are the characteristic Van der Waals coefficients of the gas The additional pressure by intermolecular forces of attraction is described by a, b represents the volume of molecules In real gases the intrinsic energy U is composed of a thermocinetic a potentional component The total change of the intrinsic energy U of a real gas therefore depends not only on the temperature the molar heat C V of a gas but also on the volume The potential energy a/v in the gas is given by the work against the intermolecular forces U C V T a V Fig 3: Temperature differences measured at various ram pressures the total differential of the intrinsic energy is given by du a 0U 0T b dt a 0U V 0V b dv T if the total differential is substituted through differences, you get U C V T a V V with a 0U 0T b C V a 0U 0V b a V for V = 0 for T = 0 with U T C V U V a V for V = 0 for T = 0 The expansion of the gas at the throttle-point is adiabatic ( Q = 0) If external heat losses friction during the flow of the gas are excluded, the total energy H of the process is constant H U p V U 1 p 1 V 1 U p V For further calculations pressure p can be substituted by using van der Waals equation Fig : Throttling the H C V T a V a R T V b a V b V P30600 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co KG D Göttingen

4 LEP 306 The relationship between T an V is given by the total differential of this equation H C V T a R V V V V b H = 0 because H is constant For the next step b is neclected against V The molar heat at constant volume C v should be replaced by the molar heat at constant pressure C p This could be done approximately by the equation for ideal gases Then C p C V R T R T b a V V C p At the throttle point a pressure gradient p 1 p a temperature gradient T 1 T are established This effect is named the Joule Thomson effect is described by the coefficient m T 1 T T p 1 p p To get this coefficient, the difference V has to be changed into p This could be done approximately by the equation for ideal gases V R T p by differentiation an substitute total differentials by differences again you get V R T p p T V V C p 1R T b a T R T p p The Joule Thomson coefficient is then m T p 1 C p a a RT b b R T V R T T V 1V b V b V H a C V R V a R T b b T a V b V 1V b b V In real gases, the intrinsic energy U is composed of a thermokinetic content a potential energy content: the potential of the intermolecular forces of attraction This is negative tends towards zero as the molecular distance increases In p C p R T b a R T real gases, the intrinsic energy is therefore a function of the volume, : U V 7 0 During adiabatic expansion ( Q = 0), during which also no external work is done, the overall intrinsic energy remains unchanged, with the result that the potential energy increases at the expense of the thermokinetic content the gas cools At the throttle point, the effect named after Joule-Thomson is a quasi-stationary process A stationary pressure gradient p p 1 is established at the throttle point If external heat losses friction during the flow of the gas are excluded, then for the total energy H, which consists of the intrinsic energy U displacement work pv: H 1 = U 1 + p 1 V 1 = U + p V = H In this equation, p 1 V 1 or p V is the work performed by an imaginary piston during the flow of a small amount of gas by a change in position from position 1 to or position 3 to 4 (see Figure ) In real gases, the displacement work p 1 V 1 does not equal the displacement work p V ; in this case: p 1 V 1 < p V This means that, from the molecular interaction potential, displacement work is permanently done removed: U 1 > U T 1 > T or The is described quantitatively by the coefficients m T 1 T p 1 p For a change in the volume of a Van der Waals gas, the change in intrinsic energy is U a V V the Joule-Thomson coefficient is thus m VDW a a RT b b 1 c p In this equation, c p is the specific heat under constant pressure, a b are the Van der Waals coefficients If the expansion coefficients a 1 V 0 V T are inserted, then m VdW VT c p a a 1 T b (p = const) PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co KG D Göttingen P

5 LEP 306 The measurement values in Fig 3 give the straight line gradients m CO = (1 084 ± 0050) 10 5 K m N = (053 ± 0030) 10 5 K The two temperature probes may give different absolute values for the same temperature This is no problem, as only the temperature difference is important for the determination Joule-Thomson coefficients The literature values are m CO = at 0 C 10 5, m air = at 0 C 10 5 K K For CO, with a = 360 m 6 /mol b = 47 cm 3 /mol c p = 3661 J/mol K the Van der Waals equation gives the coefficient m VdW, CO = K For air, with a = 140 m 6 /mol b = 391 cm 3 /mol c p = 889 J/mol K the Van der Waals equation gives the coefficient m VdW, air = K Remarks The formula for the Joule Thomson coefficient gives the condition for a cooling process: T i a R b is the inversion temperature If p < 0 the temperature T has to be lower then T i to cool gas with the process: p < 0 T < T i then T < 0 For air (N ) or CO cooling is observed at room temperatur H or He have a positive coefficient at room temperature, for H this can be hazardous because self ignition is possible 4 P30600 PHYWE series of publications Laboratory Experiments Physics PHYWE SYSTEME GMBH & Co KG D Göttingen

Table of Contents. Experiment 1: Vapour Pressure of Water at High Temperature 2. Experiment 2: Heat Capacity of Gases 5

Table of Contents. Experiment 1: Vapour Pressure of Water at High Temperature 2. Experiment 2: Heat Capacity of Gases 5 1 Table of Contents EXPERIMENT PAGE Experiment 1: Vapour Pressure of Water at High Temperature 2 Experiment 2: Heat Capacity of Gases 5 Experiment 3: Joule-Thomson Effect 11 Experiment 4: Thermal and Electrical