Equations of State (EoS) are functions that relate the variables of a thermodynamics state to one another. For pure substances they are of the form p = f(T,V,n) (3) where p, T, V, and n are pressure, temperature, volume, and moles. Often EoS are written in their molar volume form, p = f(T,V) where V = V/n. Use the following molar EoS for gases. Assume an constant temperature such that pressure is a single variable function of molar volume, p(V). RT Pia(V) V RT a Podw (V) v? V – b where R is the gas constant and a and b are constants. (a) The work done by isothermal expansion of a gas can be calculated by W = Use Eq. 4 to obtain expression for work done for an ideal gas and van der Waals gas expanding from its initial V¡ to final volume Vf. (b) Using your expressions in (a), calculate the magnitude of work done by one mole of methane in 0.250 L expanded to twice its volume 0.500 L at 300 K for the ideal and van der Waals EoS with a = 2.3026 dm · bar · mol-2 and b = 0.043067 dm3 . mol-1. Which EoS did more work? (c) Repeat your calculation in (b) for helium where a = 0.034598 dm6 · bar · mol-2 and b = 0.023733 dm · mol-. Which EoS did more work? (d) Compare your results from (b) and (c) for the van der Waals gas expansion of methane and helium. Which gas did more work?
Equations of State (EoS) are functions that relate the variables of a thermodynamics state to one another. For pure substances they are of the form p = f(T,V,n) (3) where p, T, V, and n are pressure, temperature, volume, and moles. Often EoS are written in their molar volume form, p = f(T,V) where V = V/n. Use the following molar EoS for gases. Assume an constant temperature such that pressure is a single variable function of molar volume, p(V). RT Pia(V) V RT a Podw (V) v? V – b where R is the gas constant and a and b are constants. (a) The work done by isothermal expansion of a gas can be calculated by W = Use Eq. 4 to obtain expression for work done for an ideal gas and van der Waals gas expanding from its initial V¡ to final volume Vf. (b) Using your expressions in (a), calculate the magnitude of work done by one mole of methane in 0.250 L expanded to twice its volume 0.500 L at 300 K for the ideal and van der Waals EoS with a = 2.3026 dm · bar · mol-2 and b = 0.043067 dm3 . mol-1. Which EoS did more work? (c) Repeat your calculation in (b) for helium where a = 0.034598 dm6 · bar · mol-2 and b = 0.023733 dm · mol-. Which EoS did more work? (d) Compare your results from (b) and (c) for the van der Waals gas expansion of methane and helium. Which gas did more work?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Transcribed Image Text:Equations of State (EoS) are functions that relate the variables of a thermodynamics state to one
another. For pure substances they are of the form
p = f(T,V,n)
(3)
where p, T, V, and n are pressure, temperature, volume, and moles. Often EoS are written in their
molar volume form, p = f(T,V) where V = V /n. Use the following molar EoS for gases. Assume
an constant temperature such that pressure is a single variable function of molar volume, p(V).
RT
Pia(V)
V
RT
a
Podw (V
V - b
v?
where R is the gas constant and a and b are constants.
(a) The work done by isothermal expansion of a gas can be calculated by
W =
(4)
Use Eq. 4 to obtain expression for work done for an ideal gas and van der Waals gas expanding
from its initial V; to final volume Vf.
(b) Using your expressions in (a), calculate the magnitude of work done by one mole of methane
in 0.250 L expanded to twice its volume 0.500 L at 300 K for the ideal and van der Waals EoS
and b = 0.043067 dm · mol-. Which EoS did more work?
-2
with a =
2.3026 dmº · bar · mol
0.034598 dm . bar mol-2 and b = 0.023733
(c) Repeat your calculation in (b) for helium where a =
dm3 · mol-1. Which EoS did more work?
(d) Compare your results from (b) and (c) for the van der Waals gas expansion of methane and
helium. Which gas did more work?
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