10_1425_web_Lec_34_GasProcessesHeatTransport

10_1425_web_Lec_34_G - Gas Processes and Heat Transport Physics 1425 Lecture 34 Michael Fowler UVa The First Law of Thermodynamics A closed system

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Gas Processes and Heat Transport Physics 1425 Lecture 34 Michael Fowler, UVa
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The First Law of Thermodynamics A closed system has a total internal energy E int . This energy can be changed in two different ways: A. The system can do work W , or have work done on it, - W. B. Heat Q can flow into the system, or - Q flow out. The First Law is just total energy conservation: Δ E int = Q W Change in internal energy = heat in – work done.
Background image of page 2
States of an Ideal Gas Suppose we have n moles of an ideal gas in equilibrium in a piston. The “state” of the gas can be defined by giving the state variables P , V. The gas state is a point in the ( P , V ) plane . If heat is exchanged or work done, the gas state variables trace a path in the ( P , V ) plane. If the gas moves along an isotherm PV = constant , its internal energy stays the same. Z P V The temperature (and therefore internal energy) is constant along an isotherm, PV = const.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Gas Does Some Work The gas pressure P means the force from the gas on the piston, of area A , is PA . This means that if the piston moves up a distance d , the work done by the gas, force x distance = PAd = PdV. The work done by the gas in expanding isothermally , along PV = nRT , is a Area A d BB AA B A ln VV nRT V W PdV dV nRT = = = ∫∫
Background image of page 4
States of an Ideal Gas Note that the work done by the gas in isothermal expansion is just the area under the path and in fact this must be true of the work done along any path. The gas clearly does less work going from A to B on the red path. This means less heat is supplied to the gas along the red path! Z BB AA B A ln VV nRT V W PdV dV nRT = = ∫∫ P V V A V B P V V A V B A B
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Clicker Question What is the true heat difference between state A and state B? A. The heat needed to get from state A to state B along the isotherm. B. The heat supplied going along the red route. C. The heat needed along a minimal heat transfer route, which may be different from either. D. The question doesn’t make sense. Z P V V A V B P V V A V B A B
Background image of page 6
Specific Heats of a Mole of Ideal Gas: C V If we heat up a gas by 1 ° C at constant pressure , it will expand and do work, so we must supply more heat (to do this work) than if it is heated by 1 ° C when kept at constant volume . Recall that the internal energy of a mole of gas is E int = N A kT = RT . Therefore, the heat energy input to raise the temperature 1 ° C at constant volume, the constant volume specific heat C V is just C V = R ( R = 8.3 J/mol∙K)
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Specific Heats of a Mole of Ideal Gas: C P The constant volume specific heat C V is just C V = R ( R = 8.3 J/mol∙K) For one mole of gas, PV = RT , so at constant pressure P Δ V = R Δ T = R for a temperature increase of 1 ° C (or equivalently 1K).
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/07/2011 for the course PHYSICS 1425 taught by Professor Michaelfowler during the Spring '10 term at UVA.

Page1 / 30

10_1425_web_Lec_34_G - Gas Processes and Heat Transport Physics 1425 Lecture 34 Michael Fowler UVa The First Law of Thermodynamics A closed system

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online