Lecture 1: Zeroth and First Law

Question 1

zeroth law of thermodynamics

Answer 1

if two systems are separately in thermal equilibrium with a third, then they must also be in thermal equilibrium with each other

Question 2

zeroth law leads to the concept of

Answer 2

temperature as a measurable quantity

Question 3

the zeroth law legitimises the use of

Answer 3

thermometers and calibration of temp

Question 4

what is thermal equilibrium

Answer 4

bulk physical properties are uniform and invariant

in particular, the state variables are unchanged

Question 5

example: PV curves for 2 gases in thermal equilibrium

Answer 5

get isotherms for each
hence shows property of temp can be identified

Question 6

the empirical temperature

Answer 6

a function θB(PB, VB) - an equation of state - whose value is the same for two thermally equilibrated systems.

Question 7

makes sense to define θ(P,V) as

Answer 7

linearly increasing with ‘hotness’ but it makes sense to do so by defining a scale based on a thermometric property ‘X’ and two arbitrary fixed points θ1 and θ2

Question 8

first law in differential form

Answer 8

dU=δQ+δW

Question 9

dU is

Answer 9

the infinitesimal change in internal energy (in J) for a process

Question 10

δQ is

Answer 10

the infinitesimal heat (thermal energy in J) transferred in the process.

Question 11

δW is

Answer 11

the infinitesimal work (in J) done by the surroundings on a system during the process

Question 12

what kind of differential is dU

Answer 12

exact differential
U is a function of state so ΔU is path independent

Question 13

what type of differentials are δQ and δW

Answer 13

inexact differentials

neither are uniquely defined for a process and depend on path taken between initial and final states

Question 14

inexact differentials often relate to

Answer 14

irreversible processes

Question 15

the first law tells us that although the distribution between heat (thermo) and work (dynamics) can’t always be determined,

Answer 15

their combination (thermodynamics) is calculable: U is state function

Question 16

what can we do to calculate alternative paths with well defined δQ and δW and hence explore ΔU

Answer 16

choose quasistatic, reversible processes

Question 17

1st law calculation - typical situation

Answer 17

frictionless piston compressing a fluid

Question 18

we consider reversible changes from state (P1,V1) to state (P2, V2) by

Answer 18

applying a force to the piston

Question 19

we treat applying a force to the piston as

Answer 19

a quasistatic process (do it slowly, one dx then find eqbm, then another dx, another eqbm etc)

Question 20

make applying force to a piston a reversible process by

Answer 20

neglecting frictional dissipation

Question 21

for the reversible process, the incremental work done by the surroundings on the gas is given by

Answer 21

δW=-PdV

Question 22

why is there a negative sign in δW=-PdV

Answer 22

by the surroundings on gas

gas compressed (surroundings doing work)

volume decreases

(+ve if gas doing work on surroundings)

Question 23

δW=-PdV for the complete process

Answer 23

ΔW=- ∫ PdV

Question 24

ΔW is

Answer 24

path dependent (area under curve so depends on process for path taken)

Question 25

the work done by the surroundings increases the

Answer 25

system's internal energy

Question 26

a reduced volume, increased pressure corresponds to

Answer 26

a positive ΔW

Question 27

adiabatic

Answer 27

no exchange of thermal energy