Calorimetry

Heat

CALORIMETRY (return to CONTENTS)

HEAT INVOLVED IN CHANGES OF TEMPERATURE (return to start of page)
(sometimes called ‘sensible heat’)

Heat capacity

The heat capacity of a body is the heat required to raise the temperature of the body by 1⁰C (or by 1K)

We see later, from the definition of a kelvins (K), that a temperature change of 1⁰C = a temperature change of 1K.
Thus, the unit of heat capacity can be expressed as J⁰C^-1 or JK^-1

Specific heat capacity, c

The specific heat capacity of a substance is the heat required to raise the temperature of unit mass of the substance by 1⁰C (or by 1K)

The term ‘specific’ here means ‘per unit mass’, which means per kg, in SI units (though we often also use 'per gram').

SI unit: J/(kg ⁰C) º Jkg^{-1 0}C^-1 or J/(kgK) º Jkg^-1 K^-1

Rearranging, we get:

It is not essential to put the ‘D ’ in, and some prefer to write the equation as:

Example

The temperature of a 500g body rises from 15⁰C to 20⁰C.

a) How much heat is absorbed?
b) What is the heat capacity of the body?

(c = 400 J/(kg ⁰C)

Example

A 1kg piece of aluminium at 80⁰C is immersed in 2kg of water at 15⁰C. Assuming that no heat is lost to the surroundings, what will be the final temperature of the water?
(for Al, c = 908 J kg^-1K^-1; for water, c = 4200 J kg^-1K^-1)

Example

An electric kettle contains 1.5kg of water at 21⁰C. To bring the water to the boil takes 3 minutes 46 seconds. Determine:

the heat absorbed by the water
the power of the electric element (recall that power (W) = energy (J)/time (s))

(for water c = 4200 J/(kg ⁰C)

Determination of specific heat capacity

HEAT INVOLVED IN CHANGES OF STATE (OR PHASE) (return to start of page)
(called ‘latent heat’)

There are three familar states of matter - solid, liquid and gas (or vapour). Many substances (e.g. water) can change from one state to another:

Suppose that a piece of ice, initially at –50⁰C, is continuously slowly heated. An ‘ideal’ graph of temperature against time (not drawn to scale) would look like:

Changes of phase occur at fixed temperatures. We know that water melts (and freezes) at 0⁰C and boils at 100⁰C. On the graph this means that we get flat sections during the changes of phase – as the temperatures are fixed. But the sample is being steadily heated all the time. This means that during a change of phase, all the heat supplied is used to bring about the change, and none is used to raise the temperature.

The heat involved in a change of state is called latent or ‘hidden’ heat because it does not ‘reveal’ itself as a change in temperature.

Definitions

Specific latent heat of fusion, L_f

The specific latent heat of fusion of a substance is the heat required to change unit mass of the substance from solid to liquid without change of temperature

Specific latent heat of vaporisation, L_v

The specific latent heat of vaporisation of a substance is the heat required to change unit mass of the substance from liquid to vapour without change of temperature

Example

Fifty grams of ice is at 0⁰C. How much total heat is needed to change it to steam at 100⁰C?
For ice L_f = 330 J/g; for water c = 4.2 J/(g⁰C) and L_v = 2300 J/g

There are three separate events:

VAPOURS (return to start of page)

Saturated vapour pressure

If a liquid is placed in a closed container, as above, molecules will escape from the liquid (evaporate) to become vapour molecules. Also, molecules in the vapour are moving in all directions, and some will re-enter the liquid. Eventually a state of dynamic equilibrium will be reached, at which:

When this state is reached, the vapour is said to be ‘saturated’, and the pressure it exerts is called its saturated vapour pressure (‘SVP’). Thus,

The saturated vapour pressure of a substance is the pressure of its vapour when it is in equilibrium with its liquid

If the above container were heated, more molecules would escape from the liquid, increasing the pressure of the vapour - a new dynamic equilibrium would be established at the higher temperature. Thus, SVP rises with temperature.

For water:

Note: A gas below a certain temperature, called its critical temperature, is called a vapour. A vapour can be liquified by increasing the pressure on it without changing its temperature. In the previous diagram, if the system were in equilibrium at a certain temperature, and then the container were compressed a little, enough vapour would liquify to keep the number of vapour molecules per cm³, and therefore the vapour density and pressure, constant.

Boiling

Boiling occurs at a particular temperature, and consists of the formation of bubbles of vapour throughout a liquid.

For a bubble to exist:

Thus, the boiling point of a liquid is the temperature at which its SVP equals the external pressure - and this is 100⁰C for water, as shown in the previous graph.

Evaporation

When a liquid evaporates it changes to vapour without reaching its boiling point.

The molecules in a liquid are in constant motion. Those near the surface can actually jump out of the liquid. Most will fall back, but some will escape to become vapour molecules. This is evaporation.

A pool of water evaporates most quickly (and clothes on a line dry most rapidly) when:

it's sunny
it's breezy
there is little water vapour in the atmosphere (low humidity)

The sunshine gives molecules near the surface of a liquid extra kinetic energy ('KE') and so they can jump further out of the liquid. If it is breezy molecules jumping out of the liquid are simply blown away.

Cooling by evaporation

Molecules in a liquid are all moving, but with a variety of speeds, and so a variety of kinetic energies
The temperature of a liquid depends on the average KE of its molecules
It is the molecules near the surface with the greatest KE which are most likely to escape into the air
Since it is the most energetic molecules that escape during evaporation, the average KE of the ones left behind must fall, so the temperature of the liquid must fall

The body makes use of this 'cooling by evaporation' – sweat evaporates, taking heat from the body.

The refrigerator

The pipe contains a volatile liquid (E.g. Freon) – ‘volatile’ meaning it has a low boiling point (below 30⁰C), so it readily vaporises.

The pump reduces the pressure over the liquid, encouraging it to vaporise. As it does so, it takes latent heat in from its surroundings, cooling the ice box
The vapour is compressed by the pump and turns back to liquid, giving latent heat out. It does this at the cooling fins on the outside of the fridge at the back (these have a large area and are painted black)
An adjustable thermostat switches the pump on and off, controlling the temperature

Evaporation and boiling compared

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