Instructor Name Dr Zain Yamani Director of CENTKFUPM

ﺍﻟﺪﻳﻨﺎﻣﻴﻜﺎ ﺍﻟﺤﺮﺍﺭﻳﺔ ﻭﺍﻟﻤﻴﻜﺎﻧﻴﻜﺎ ﺍﻹﺣﺼﺎﺋﻴﺔ ﻟﻠﻐﺎﺯﺍﺕ ﺍﻟﻤﺜﺎﻟﻴﺔ Instructor: Name: Dr. Zain Yamani Director of CENT-KFUPM [www. kfupm. edu. sa/cent] Phone: 013 -860 -4363 Mobile: 0504608515 E-mail: zhyamani@kfupm. edu. sa Time of meetings: Saturdays 9. 30 – 11. 30 a. m. ﺍﻟﻤﺤﺎﺿﺮﺓ ﺍﻟﺜﺎﻟﺜﺔ ﻫـ 1439 ، ﺭﺟﺐ 14

Sumayyah. . Gaussian integral using Gamma function

Now, let’s study the Ideal Gas

Describe the state of equilibrium of an ideal gas • • • Pressure, Volume, Temperature, Number of molecules, Internal energy, Collisions, Equilibrium, Entropy, Heat capacity, Molecular speed, …

What are the assumptions of an “ideal” gas? Physics for Scientists and Engineers (by Serway)

Are real gases ideal? When do real gases behave like ideal gases?

Boyle: pressure is inversely proportional to volume (at constant temperature) Charles: volume is proportional to temperature (at constant pressure) Gay-Lussac's law: pressure is proportional to temperature (at constant volume) p V = n R T R = N/n k = NA k p V = N k T The ideal gas ‘law’ is an experimental finding that is more accurate for high temperatures and low densities (large V/n)

For a wide range of problems with gases, it is safe to use P V = n R T Can we now try to figure out what the internal energy of a monatomic ideal gas is in relation to P, N, V, and T?

½ m v 2 rms= 3/2 k T U = 3/2 N k T vrms= (3 R T/M)0. 5 Example: A tank of volume 0. 3 m 3 contains 2 moles of helium gas at 20 o. C. a. Find the total internal energy of the system. b. What is the average kinetic energy per molecule? c. Find the rms speed of the molecules Example taken from Serway

Isotherms of the Ideal Gas P = (n R T)/V The ideal gas law gives a hyperbolic relation in the P-V plane

Hyperbolic Isotherms of the Ideal Gas