Thermodynamics

Temperature

What is temperature?

Temperature is what we measure with a thermometer.

What is a thermometer?

A thermometer is any devise that has an observable and measurable property that changes in response to a change in the temperature of the device… Thermometric Property

How does a thermometer measure temperature?

The operation of a thermometer is based on the Zeroth Law of Thermodynamics

A thermometer can only measure its own temperature.

Zeroth Law of Thermodynamics

“If two objects initially at different temperatures are placed in thermal contact, their temperatures will change until they

are at the same equilibrium temperature”This condition is called thermal equilibrium.”

TH > TC

TH > Teq> TC

thermal equilibrium reached

TH TC

TeqTeq

TH TC↓ ↑

To measure the temperature of an object a thermometer is placed in thermal contact with the object. Once the thermometer and object have reached thermal equilibrium it can be assumed that the temperature of the thermometer is equal to the temperature of the object.

How do we measure the temperature of the thermometer?

It must be calibrated with systems whose temperatures are known or defined.

Two systems that are commonly used are:

1. A mixture of ice and water.

2. Boiling water

These systems are used because it has been observed that as long as ice and water are present together the temperature remains constant, and as long as water is boiling its temperature remains constant.

The temperature of a mixture of ice and water is defined to be:0 degrees Celsius, 0°C or 32 degrees Fahrenheit, 32°F.

The temperature of boiling water is defined to be:100 degrees Celsius, 100°C or 212 degrees Fahrenheit, 212°F.

Consider the calibration of a liquid-in-glass thermometer.

Liquid-in-Glass Thermometer

glass housing

capillary

liquid reservoir

The thermometric property is the height of the liquid in the capillary

As the temperature of the thermometer changes, the liquid in the reservoir expands or contracts causing the level of the liquid in the capillary to rise or fall.

Once the temperature of the thermometer becomes constant the level of the liquid will be constant.

What temperature corresponds to this level of liquid?

T =?

Calibration of a Liquid-in-Glass Thermometer

Insert the thermometer into a container holding a mixture of ice and water and wait for thermal equilibrium to be reached.

Height of liquid has

fallen.

0°C32°F

Place a “mark” on the thermometer where the liquid stopped moving and label with the defined temperature of ice/water (0°C or 32°F)

ThermalEquilibrium

reached

Insert the thermometer into a container holding boiling water and wait for thermal equilibrium to be reached.

Height of liquid has risen.

Source of heatTo keep water

boiling

0°C32°F

Place a “mark” on the thermometer where the liquid stopped moving and label with the defined temperature of boiling water (100°C or 212°F)

100°C212°F

ThermalEquilibrium

reached

0°C32°F

100°C212°F

Determine how the height of the liquid relates to the temperature.

Temperature, °C

Height, cm

The slope of the graph = ΔhΔT =constant

The space between the two marks can be divided into equally spaced divisions:

100 divisions for Celsius (each division = 1C°) or

180 divisions for Fahrenheit (each division = 1F°) .

Temperature Scales

Steam Point

Ice Point

Absolute Zero

Fahrenheit

-459°F

32°F

212°F

Celsius

-273°C

0°C

100°C

Kelvin

0 K

273 K

373 K

Temperature Conversions

Celsius to Fahrenheit TF =95 TC +32 =1.8TC + 32

Fahrenheit to Celsius TC =59 TF −32( ) ≈.56 TF − 32( )

Celsius to Kelvin TK =TC +273

Kelvin to Celsius TC =TK −273

Example

Convert 77K (temperature of liquid nitrogen) to Fahrenheit.

TC =TK −273 =77 −273 =−196°C

TF =1.8TC + 32 =1.8 −196( ) + 32 =

−352.8 + 32 = −320.8°F