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The molecules of a certain ideal gas consist of three atoms arranged in a non-linear way, i.e., the atoms do not lie in a straight line. This is shown in the fiøure. * . where X,Y, Z represent the co-ordinates of a co-ordinate system whose origin is at the centre of mass of the molecule. This lies close to the most massive atom in the molecule. Let m be the mass of each molecule. (a) Theoretically, at moderately high temperatures, e.g. room tem- perature, a molecule of the gas mentioned above moves in the X, Y, Z directions and rotates about the X,Y, Z axes. Stating your assumptions i. Find an expression for the average energy of a molecule. ii. Find an expression for the internal energy of the gas. iii. Show that Cp/Cy for the gas is 4/3.

The molecules of a certain ideal gas consist of three atoms arranged in a non-linear way, i.e., the atoms do not lie in a straight line. This is shown in the fiøure. * . where X,Y, Z represent the co-ordinates of a co-ordinate system whose origin is at the centre of mass of the molecule. This lies close to the most massive atom in the molecule. Let m be the mass of each molecule. (a) Theoretically, at moderately high temperatures, e.g. room tem- perature, a molecule of the gas mentioned above moves in the X, Y, Z directions and rotates about the X,Y, Z axes. Stating your assumptions i. Find an expression for the average energy of a molecule. ii. Find an expression for the internal energy of the gas. iii. Show that Cp/Cy for the gas is 4/3.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The molecules of a certain ideal gas consist of three atoms arranged in a non-linear way, i.e., the atoms do not lie in a straight line. This is shown in the fiøure. X. where X, Y, Z represent the co-ordinates of a co-ordinate system whose origin is at the centre of mass of the molecule. This lies close to the most massive atom in the molecule. Let m be the mass of each molecule. (a) Theoretically, at moderately high temperatures, e.g. room tem- perature, a molecule of the gas mentioned above moves in the X,Y, Z directions and rotates about the X,Y, Z axes. Stating your assumptions i. Find an expression for the average energy of a molecule. ii. Find an expression for the internal energy of the gas. iii. Show that Cp/Cy for the gas is 4/3. (b) Under what circumstances would Cp/Cy be less than 4/3? (c) Suppose the gas is not an ideal gas, but a real gas. The gas' van der Waal's constants are: a = 0.4544 N m* mol-2 and b 4.339 x 10-5 m³ mol¬1. There are 0.1 mol of the gas and initially it occupies 50 x 10-6 m³ when the pressure is 50 atm. i. What is the initial temperature of the gas? ii. Determine the pressure of the gas after being compressed at constant temperature to a volume of 30 × 10-6 m³ .
Transcribed Image Text:The molecules of a certain ideal gas consist of three atoms arranged in a non-linear way, i.e., the atoms do not lie in a straight line. This is shown in the fiøure. X. where X, Y, Z represent the co-ordinates of a co-ordinate system whose origin is at the centre of mass of the molecule. This lies close to the most massive atom in the molecule. Let m be the mass of each molecule. (a) Theoretically, at moderately high temperatures, e.g. room tem- perature, a molecule of the gas mentioned above moves in the X,Y, Z directions and rotates about the X,Y, Z axes. Stating your assumptions i. Find an expression for the average energy of a molecule. ii. Find an expression for the internal energy of the gas. iii. Show that Cp/Cy for the gas is 4/3. (b) Under what circumstances would Cp/Cy be less than 4/3? (c) Suppose the gas is not an ideal gas, but a real gas. The gas' van der Waal's constants are: a = 0.4544 N m* mol-2 and b 4.339 x 10-5 m³ mol¬1. There are 0.1 mol of the gas and initially it occupies 50 x 10-6 m³ when the pressure is 50 atm. i. What is the initial temperature of the gas? ii. Determine the pressure of the gas after being compressed at constant temperature to a volume of 30 × 10-6 m³ .
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