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USSC2001 Energy Lecture 3 Thermodynamics of Heat. Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543. Email matwml@nus.edu.sg http://www.math.nus/~matwml Tel (65) 6874-2749. 1. TUTORIAL 3.

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ussc2001 energy lecture 3 thermodynamics of heat

USSC2001 Energy Lecture 3 Thermodynamics of Heat

Wayne M. Lawton

Department of Mathematics

National University of Singapore

2 Science Drive 2

Singapore 117543

Email matwml@nus.edu.sg

http://www.math.nus/~matwml Tel (65) 6874-2749

1

slide2

TUTORIAL 3

1. In problem 2, tutorial 2, (i) show that angles a1, a2 opposite sides with lengths 1m,2m are not determined but the ratio sin(a1)/sin(a2) is determined and compute it, (ii) let M denote the mass of the object on the side having length 2m and express the change of total gravitational potential energy if the system has a ‘virtual displacement’ in which the object with mass M moves by distance d downwards, (iii) explain the “Principle of Virtual Work” and use it to compute the value of M if the system is in equilibrium, (iv) discuss Simon Stevinus and use his method to compute M.

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Stevin.html

http://3quarksdaily.blogs.com/3quarksdaily/2005/05/monday_musing_s.html

2

slide3

WHAT IS THERMODYNAMICS?

Read chapter 19 (handouts) of Halliday, Resnick and Walker, study Review&Summary and Problems.

Deals with thermal (internal) energy and involves the concept of temperature, an elusive property of objects that alters apparent properties, including lengths & volumes and electrical resistance, any of which can be used to make a thermoscope (not yet a thermometer).

Zeroth Law of Thermodynamics: If bodies A and B are each in thermal equilibrium with a third body T, then they are in thermal equilibrium with each other.

3

slide4

DEFINING TEMPERATURE

The triple point of water

http://en.wikipedia.org/wiki/Triple_point

degrees Kelvin

Pascals

We define the temperature of a gas by

Here we use the fact that T is the same for ALL gases.

4

slide5

CONSTANT-VOLUME GAS THERMOMETER

The ingenius mercury thermometer shown below (page 428 in HRW) can measure T at constant volume

Questions How is constant volume maintained at different temperatures? How is density measured?

Gas-filled bulb

Reservoir that can be raised and lowered

5

slide6

TEMPERATURE SCALES

All scales are inter-related by affine functions

And therefore determined by their values at

absolute zero and the triple point of water

Absolute zero

Triple point

Question Compute the values of a and b for the six

affine functions that convert

K  C, K F, C K, C F, F K, F C

6

slide7

IDEAL GAS LAW

Amadeo Avogado 1776-1856 suggested that all

gases contained the same number of molecules

for a fixed volume, pressure and temperature

moles

molecules =

where

= # molecules in a mole

= the Boltzmann constant

= the gas constant

Question How are k and R related?

7

slide8

TUTORIAL 3

2. Newton’s 3rd Law states: When 2 bodies (particles) interact, the forces on the bodies from each other are always equal in magnitude and opposite in direction. The (linear) momentum of a body is defined to be the product of its mass times its velocity and the momentum of a system is the ‘sum of its parts’ (i) use Newton’s laws to show that when 2 bodies interact (eg in a collision) the system momentum is conserved, (ii) compute the average pressure that a molecule with kinetic energy E_kin exerts on a cubic container with volume V, (iii) combine this and the ideal gas law to show average molecular kinetic energy = 3kT/2

8

slide9

TEMPERATURE AND HEAT

Thermal or internal energy consists of kinetic and energies associated with their random motions and, especially for solids and liquids, the potential energy due to their proximity.

Heat Q is thermal energy transferred to a system from its environment, Q > 0, Q < 0 when the system temperature is lower, higher than environment’s, it can be associated with a change of temperature

where m=mass and c = specific heat capacity of a material (c=4190J/(kg K for water at 14.5C) or with

a change of phase (heats of fusion and vaporization).

9

slide10

HEAT TRANSFER MECHANISMS

Heat can be transferred by conduction

convection, and radiation

Questions What are the constants in these equations?

10

slide11

insulation

lead shot

WORK AND HEAT

W

pressure

state

diagram

Q

volume

thermal reservoir

W (and Q) depend on the thermodynamic process, described by a path, not only on initial&final states

11

slide12

THERMODYNAMIC PROCESSES

As shown on p 438-439 in HRW, W = the work done by a system is path dependent, this is also true for Q = heat transferred to the system since, as stated in lines 6-8 from bottom page 435 that gases have different values for their specific heats under constant-pressure and under constant-volume conditions.

Question Compute W for constant p and constant T

12

slide13

FIRST LAW OF THERMODYNAMICS

There exists an internal energy function

such that during any thermodynamic process

The first law is illustrated for adiabatic (Q=0), constant volume (W = 0), and closed cycle or cyclic processes on page 441 of HRW. Free expansion on page 442 differs from all other processes why?

13

slide14

SECOND LAW OF THERMODYNAMICS

There exists an entropy function

such that during any thermodynamic process

or, equivalently, such that

14

slide15

TUTORIAL 3

3. Combine the formular

with

the ideal gas law and the eqn.

where

moles of a quantity of gas

and

molar specific heat at constant volume

to show that for an ideal gas

4. Find out what a Carnot Cycle is and how it differs from a Stirling Cycle. What is more efficient?

5. What is free energy and how does it explain

the thermodynamics of chemical reactions?

15