# Thermodynamic Investigation of the Joule-Thompson Effect

Niki Spadaro, Megan Cheney, and Jake Lambeth

University of North Florida, CHM4410C Fall 2010

The Joule-Thomson coefficient explains the behavior of any real gas when changes in intensive properties, such as temperature and pressure, occur. The coefficients for helium and carbon dioxide were determined using a Joule-Thomson apparatus that created constant enthalpy within the system. Using literature values for the coefficients at room temperature, the experimental results allow examination of each gas’s unique nature.

Introduction

Enthalpy is a critical study in thermodynamics. It is a measurement of a system’s internal energy (U) and work associated with pressure and volume: H = U + PV (1) Isenthalpic conditions were established in the experiment by use of the Joule-Thomson apparatus, in which a glass filter divided a glass cylinder into two chambers. This constant enthalpy can be explained by a series of equations that apply to the system. (Smith, pp.125-127).

The First Law of Thermodynamics describes the internal energy of a system as a function of transferred heat (q) and P-V work (w) done: ∆U = dq + dw = dq - PdV (2) Since the experimental procedure was conducted in an adiabatic environment, no heat transfer occurred and the internal energy depended only on work. The total work of the system is the sum of the work done on each side of the chamber to maintain equilibrium. The latter statements allow alteration of equation 2: ∆U = U2 – U1 = ∑dw = dw1 + dw1 = - ∫P1dV - ∫P2dV (3) U2 – U1 = P1V1 – P2V2 (a.) ( U1 + P1V1 = U2 + P2V2 (b.) (4a,b) Incorporating equation 3b. into equation 1, it is apparent that the work being done on each side is the same. There is no occurrence of enthalpy change across the barrier: ∆H = H2- H1 = (U2 + P2V2) - (U1 + P1V1) (a.) ( H2 = H1 (b.) (5a,b) ( ∆H = 0

The Joule-Thomson coefficient can be determined via this proof of constant enthalpy and alteration of its total derivative. dH = (∂H/∂T)p dT + (∂H/∂P)T dP = 0 (6) - [(∂H/∂P)T] / [(∂H/∂T)p] = (dT/dP)H = µJ-T (7) Equation 7 demonstrates that temperature is dependent on pressure change within the adiabatic system. According to the Joule-Thomson effect, the temperature change across the barrier occurs without heat or work generation as the gas expands from a volume of high pressure to a volume of low pressure in order to maintain equilibrium. (Smith, pp.126) In the experiment, gas permeated the glass barrier as it flowed between chambers of congruent temperatures. Equation 7 also establishes an inverse relationship between the coefficient and heat capacity of a gas (Cp = (∂H/∂T)p). Since heat capacity is a material-dependent property, it varies for each element and compound, as does the coefficient. (Gould & Tobochnik, pp. 40) This value describes the nature of a gas and how it may react when presented under certain conditions.

In the conducted experiment, values were obtained for the Joule-Thomson coefficients for helium and carbon dioxide at varied temperatures. The literature values for helium and carbon dioxide under conditions of 1 atm and 298.15 K are -6.2E-5 K/hPa and 0.00109 K/hPa, respectively. (Engel & Reid, pp. 58). The results allow analysis of the molecular interactions of the gas based on its behavior. The magnitude of the coefficient describes whether the molecules work against repulsive or attractive forces upon expansion. A positive value indicates dominance in the attractive forces where the gas cools as molecules move apart, while a negative value signifies repulsive force dominance and gas warming. (Garland, Nibler & Shoemaker,...

References: 1. Engel, T. & Reid, P. Physical Chemistry, 2nd ed. 2006, Pearson Prentice Hall, New

Jersey, pp

3. Gould, H. & Tobochnik, J. Statistical and Thermal Physics (STP). 2009, Princeton University Press, New Jersey, pp. 31-106.

4. Smith, E. Basic Chemical Thermodynamics, 5th ed. 2004, Imperial College Press, London, pp. 125-128.

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