# Homework Help: Homework on temperature

1. Mar 22, 2006

### francisco

i've been reading resnick, halliday, and krane physics, volume one, fourth edition on temperature.

let system A = a liter of gas containing 3 * 10^22 molecules.
let E = the environment of A

the temperature (a macroscopic quantity) of A is related to the average kinetic energy of translation of the molecules.

let A be isolated from E (neither energy nor matter can enter or leave A). A is surrounded by walls presumed to be both rigid and impermeable (adiabatic or insulating walls).

let's now replace the adiabatic walls of A with walls (diathermic or conducting walls) that permit the flow of heat (a form of energy).

when A is placed in contact with E through diathermic walls, the exchange of heat causes the pressure of A and E to change. the change is relatively fast at first but becomes slower as time goes on until finally their corresponding pressures approach constant values (A and E are in thermal equilibrium).

if no change in pressure is observed with time, then A and E were originally in thermo equilibrium.

let A again be isolated from E. and let system B = a liter of another gas containing 2 * 10^23 molecules. let's place B in contact with A and then with E and discover that A and E separately are in thermal equilibrium with B. if that's the case, then A and E are also in thermal equilibrium (the zeroth law of thermodynamics).

when A and E are in thermal equilibrium, they have the same temperature.
temperature is that property of A which equals that of E when the two are in thermal equilibrium.

suppose A and E initially have different temperature, pressure, and volume. after we place them in contact and wait a sufficiently long time for them to reach thermal equilibrium, their pressure will in general not be equal, nor will their volume, but their temperature will always be equal in thermal equilibrium. through this argument, based on thermal equilibrium, the notion of temperature can be introduced into thermodynamics.

let's identify B as a thermometer. if B comes separately into thermal equilibrium with A and E and indicates the same temperature, then A and E are in thermal equilibrium and have the same temperature.

there exists a scalar quantity called temperature, which is a property of the thermodynamic systems A, E, and B in equilibrium. A, E, and B are in thermal equilibrium if and only if their temperature are equal (the zeroth law of thermodynamics).

the zeroth law defines the concept of temperature and specifies it as the one macroscopic property of B that will be equal to that of A or E when they are in thermal equilibrium. the zeroth law permits us to build and use B to measure the temperature of A or E, for we now know that B in thermal contact with A or E will reach a common temperature with them.

at the end of the chapter, the book asks the following question:
can we define temperature as a derived quantity, in terms of length, mass, and time? think of a pendulum, for example. what do you think? thanks!

Last edited: Mar 22, 2006
2. Mar 22, 2006

### jackiefrost

Since "temperature" is just a calibrated "yardstick" for comparing the kinetic energy (or equivalent) between systems of particles, the terms length, mass, time, are appropriate when combined with a constant of proportionality, k. The constant k would simply scale the Temperature unit (what we mean by "degree") to a definitely prescribed quantity of Energy (say, the "joule" - which is a length, mass, and time based unit). This is what was done in defining the Kelvin temperature scale. After all, it's only a quantity of energy being compared with another quantity of energy - by whatever name we give it or means we choose to quantify it.

jk

3. Mar 22, 2006

### francisco

i don't understand. can you give me an example?
let system A = a liter of gas.
let system B = a liter of another gas.
let me rephrase what you said.
temperature is a calibrated yardstick for comparing the kinetic energy between A and B.
length, mass, time are combined with a constant of proportionality, k.
k scales the temperature unit to a prescribed quantity of J.

we can say that T = kX. how do we combine length, mass, time with k?
1 J = 0.239 cal.
1 cal. = the amount of heat required to raise the temperature of water 1 C degree.
how does k scale the temperature unit to a prescribed quantity of J? i am confused.

4. Mar 22, 2006

### Hootenanny

Staff Emeritus