Worksheets/Van Der Waal Equation - Revision history

Admin: /* Worksheet Questions */

2016-05-22T03:52:59Z

Worksheet Questions

@@ Line 65: / Line 65: @@
 =Worksheet Questions=
-==Question 1: Critical Point Derivation==
+==Question 1: Steam==
 Show that the critical point <math>(P_c, V_c, T_c)</math> is given by:
@@ Line 94: / Line 104: @@
 Look up the values of a and b for carbon dioxide, and use them to calculate the critical point for carbon dioxide. Cite your source of information.

2016-05-22T03:52:42Z

Question 2: Carbon Dioxide

← Older revision		Revision as of 03:52, 22 May 2016
Line 89:		Line 89:
	Finally, you know Pc as a function of Vc and Tc.		Finally, you know Pc as a function of Vc and Tc.

	==Question 2: Carbon Dioxide==		==Question 3: Carbon Dioxide Critical Point==

	Carbon dioxide has interesting properties when supercritical, and can be used as an environmentally benign solvent in semiconductor manufacturing.		Carbon dioxide has interesting properties when supercritical, and can be used as an environmentally benign solvent in semiconductor manufacturing.

2016-05-22T03:52:29Z

Question 1: Derivation

← Older revision		Revision as of 03:52, 22 May 2016
Line 65:		Line 65:
	=Worksheet Questions=		=Worksheet Questions=

	==Question 1: Derivation==		==Question 1: Critical Point Derivation==

	Show that the critical point <math>(P_c, V_c, T_c)</math> is given by:		Show that the critical point <math>(P_c, V_c, T_c)</math> is given by:

2016-05-22T03:52:15Z

@@ Line 1: / Line 1: @@
-=Background=
+=Read This Before You Begin=
-Critical points of gas, supercritical behavior
+In this worksheet, students are getting some experience applying the concept of a partial derivative in a setting other than (x,y,z) space. Thermodynamics is an important area of application for vector calculus.
-The Van Der Waal equation for a gas accounts for non-ideal behavior caused by strong intermolecular forces of attraction or repulsion:
+(Expectations go here.)
 <math>
@@ Line 9: / Line 39: @@
 </math>
-where P is the pressure, V is the molar volume (volume of a certain number of moles), a and b are constants that depend on the molecules, k is the Boltzmann constant, and T is temperature.
+where P is the pressure, V is the molar volume (volume of a certain number of moles), a and b are constants that depend on the molecules, R is the ideal gas constant, and T is temperature.
-Now the critical points can be found: https://www.youtube.com/watch?v=VjVQxzxxLVw
+We can use this to find properties of the gas: given the volume and temperature, for example, we can find the pressure.
-Critical point is the saddle point of the above equation, and is defined as the point where:
+==Critical Points==
 <math>
@@ Line 24: / Line 60: @@
 \dfrac{\partial^2 P}{\partial V^2} \bigg|_{T=T_c,V=V_c} = 0
 </math>
 =Worksheet Questions=

2016-05-22T03:36:11Z

← Older revision	Revision as of 03:36, 22 May 2016
(No difference)

2016-05-22T03:36:04Z

Question 3: Steam

← Older revision		Revision as of 03:36, 22 May 2016
Line 61:		Line 61:
	In this question, you'll be investigating steam, the vapor form of water. You will compute its properties using the Van Der Waals equation, and compare the same calculation using the Ideal Gas equation, to estimate the error in assuming steam is an ideal gas.		In this question, you'll be investigating steam, the vapor form of water. You will compute its properties using the Van Der Waals equation, and compare the same calculation using the Ideal Gas equation, to estimate the error in assuming steam is an ideal gas.

	If steam has a temperature of ~~130 F~~ (~~XYZ~~ K) and a molar volume of ~~(XYZ~~ L/mol), what is the resulting pressure using the Van Der Waals equation?		If steam has a temperature of 150 C (423.15 K) and a molar volume of 7.002 L/mol, what is the resulting pressure using the Van Der Waals equation?

	What is the resulting pressure using the Ideal Gas equation?		What is the resulting pressure using the Ideal Gas equation?

	What is the relative (percent) error in the ideal gas approximation?		What is the relative (percent) error in the ideal gas approximation?

2016-05-22T03:31:23Z

Question 1

@@ Line 25: / Line 25: @@
 </math>
-=Question 1=
+=Worksheet Questions=
 Show that the critical point <math>(P_c, V_c, T_c)</math> is given by:
@@ Line 48: / Line 50: @@
 Finally, you know Pc as a function of Vc and Tc.

2016-05-22T03:20:43Z

Question 1

2016-05-22T03:20:32Z

Background

2016-05-22T03:15:41Z

Question 1

← Older revision		Revision as of 03:15, 22 May 2016
Line 40:		Line 40:
	T_c = \dfrac{8a}{27bk}		T_c = \dfrac{8a}{27bk}
	</math>		</math>

			Start by rearranging to get P as a function of T and V.

	Find the two expressions, now you have two equations and two unknowns Vc and Tc.		Find the two expressions, now you have two equations and two unknowns Vc and Tc.