Lecture 25 – Thermodynamics, HeatHeat and and temperature Temp (cont.) Gases & Kinetic theory http://candidchatter.files.wordpress.com/2009/02/hell.jpg Physics 218 Fall 2010 Specific Heat Specific Heat: heat capacity per unit mass Q CT cmT Specific Heat of Water: cal J 1 4190 ggC o kggK Physics 218 Fall 2010 Specific Heat After a grueling work out, you drink a liter of cold water (0C). How many calories does it take for the body to raise the water up to a body temperature of 36 C? cal J Specific Heat of Water: 1 4190 ggC o kggK 1 liter 1000g of H2O cal 1000g*1 *36C 36,000cal 36 Calories gC 1 pat of butter is 36 Calories 1 slice of bread (0.4 oz no crust) ~ 32 Calories Physics 218 Fall 2010 Quiz: Two blocks of equal mass but different material are placed in thermal contact. One is at 100 oC and the other at 0 oC. What temperature do they reach at thermal equilibrium? A. 100 oC B. 50 oC C. 0 oC D. Can’t tell Physics 218 Fall 2010 Phase Transitions As you add heat to water, the temperature increases for a while, then it remains constant, despite the addition of heat! Q=mL Latent Heat, L, (J/kg) is the heat which must be added to (or removed from) 1 kg of a material to change from one phase to another phase. During the conversion the temperature remains constant. Physics 218 Fall 2010 Phase Transitions Latent Heat of Fusion, LF, : Solid to Liquid Latent Heat of Vaporization, LV, : Liquid to Gas Latent Heat of Sublimation, Ls , : Solid to Gas Physics 218 Fall 2010 Phase Transitions Physics 218 Fall 2010 System complete converted to steam at 138 C. To make steam, you addExample 5.60 x105 J of heat to 0.220 kg of water at an initial temperature of 50.0 oC. Find the final temperature of the steam. Calculate heat needed to heat water to 100C: J Q mc T 0.220kg *4186 *50.0C 4.60x104 J 1 water kg *C o Calculate heat needed to convert liquid to steam: J Q mL 0.220kg * 22.6x105 4.97x105 J 2 v kg Determine Heat that is still available to add to system 5 5 5 Q3 5.60x10 J Q1 Q2 5.60x10 J 4.60x104 4.97x10 J 17,000J Use Q3 to find increase in temperature above 100C: Q3 17,000J mcsteam T Q 17,000J T 3 38C o J mcsteam 0.220kg *2010 o Physics 218 Fall 2010 kg *C Chapter 15: Gases & Kinetic Theory Physics 218 Fall 2010 Avogadro’s Number One mole = number of atoms in a 12g sample of carbon 12. How many atoms/molecules are in a mole? 1 Avogadro’s Number: N 6.02x1023 A mol Number of moles, n, contained in a sample: N n N=number of molecules in a sample N A Physics 218 Fall 2010 Atomic Mass Physics 218 Fall 2010 Molar Mass mass of molecule in “u” is numerically the same as the molar mass g/mole. Ex. O 2 molar mass: 31.998 g/mole mass of one molecule: 31.998 u Physics 218 Fall 2010 Ideal Gas Law PV NkT P: pressure V: volume N nN A N: number of molecules k: Boltzman’s constant = 1.38 x10-23 J/K R T: Temperature k nR Nk N A Physics 218 Fall 2010 Ideal Gas Law PV nRT P: pressure V: volume N nN A n: number of moles R: gas constant = 8.31 J/mol*K T: Temperature Physics 218 Fall 2010 Example One mole (1.00 mol) of Helium gas is at a room temperature of 300 K and 1.00 atm of pressure. How many Helium atoms are in each cubic millimeter of the gas? PV nRT J nRT 1.00mol * 8.315 *300K V molgK P 1.013x105 Pa 2 3 V 2.46x10 m One cubic mm = 10-9 m3 V ' 1.0x109 m3 N N *6.02x1023 atoms 2.45x1016 atoms V A 2.46x102 m3 Physics 218 Fall 2010 Ideal Gas Law PV nRT For Constant Number of molecules: PV P V 1 1 2 2 T1 T2 For Constant Number of molecules & Temperature Boyle’s Law P1V1 P2V2 Physics 218 Fall 2010 Ideal Gas Law For Constant n & T Boyle’s Law P1V1 P2V2 http://charles-boyle-law.org.ru/im/im5.jpg Physics 218 Fall 2010 Example In the morning, when the temperature is 288 K, a bicyclist finds that the absolute pressure in the tires is 505 kPa. That afternoon, she finds that the pressure in the tires has increased to 552 kPa. Ignoring expansion of the tires, find the afternoon temperature. PV P V 1 1 nR const. 2 2 T1 T2 P P 1 2 T1 T2 P2T1 552kPa *288K T2 315K P1 505kPa Physics 218 Fall 2010 Kinetic Theory of Gases Kinetic energy of a molecule 3 KE 2 B k T m2 v Kinetic energy of a molecule KE 2 k3 T Average velocity v B m Physics 218 Fall 2010 Maxwell’s Speed Distribution k3 T v B m Physics 218 Fall 2010 Molecular Speed: 3kT v rms m Escape Speed: 2GM E ve 11,200m / s RE Physics 218 Fall 2010 If the temperature of an ideal gas is doubled and the pressure is held constant, the average speed of the molecules A. remains unchanged B. is 4 times the original speed C. is 2 times the original speed D. is 2 times the original speed Physics 218 Fall 2010.