CALORIMETRYPhysics 12

Objectives Define specific heat capacity. Solve problems involving specific heat

capacities. Explain the difference between solid, liquid,

and gaseous phases. Explain in terms of molecular behavior why

temperature does not change during a phase change.

Define latent heat. Solve problems involving latent heats.

Activities Worksheet Lab demonstration: Determining the

specific heat capacity of a substance Lab demonstration: Determining the

latent heat of a substance Design lab: Design a homemade

calorimeter and test it

Specific heat capacity If heat flows into an object, its

temperature rises.

What factors might affect the magnitude of the temperature change?

Specific heat capacity The amount of energy Q required to change

the temperature of a given material is proportional to the mass m of the material and to the temperature change ΔT, shown by the simplistic expression:

Q = mc ΔT

where c is the characteristic of the material called its specific heat capacity

Specific heat capacity A high specific heat capacity means that

more energy is required to achieve the same temperature change, i.e. it is more “difficult” to raise the temperature of that material.

If a material is a good heat conductor (e.g. metals) would you expect it to have a high or low specific heat capacity?

Specific heat capacitySpecific heat capacities of specific substances

Substance Specific heat capacity, c / Jkg-

1°C-1

aluminum 900

copper 390

iron or steel 450

lead 130

wood 1700

water (ice) 2100

water (liquid) 4186

water (steam) 2010

human body (average)

3470

Specific heat capacityQ / J m / kg c / Jkg-1C-1 ΔT / °C or

°K? increased constant constant? constant constant increased

constant increased constant ?increased constant constant ?

? constant increased constant

Specific heat capacity

(a) How much heat input is needed to raise the temperature of an empty 20-kg vat made of iron from 10C to 90C?

(b) What if the vat is filled with 20 kg of water?

Specific heat capacity

(a) 720 kJ(b) 7400 kJ

Specific heat capacityYou accidentally let an empty iron frying pan get

very hot on the stove (approx. 200C). What happens when you dunk it into a few inches of cool water in the bottom of the sink?

Will the final temperature be midway between the initial temperatures of the water and pan? Will the water start boiling?

(Assume the mass of the water is roughly the same as the mass of the pan.)

Calorimetry In discussing heat and thermodynamics,

we shall often refer to systems.

What is the difference between open, closed, and isolated systems?

Calorimetry Open system

Mass and energy may leave and enter Closed system

Energy may leave and enter but mass may not Isolated system

Neither mass nor energy may leave or enter

Calorimetry We will often make the assumption that

the systems we are dealing with are isolated.

Why is this necessary?

Calorimetry In an isolated system, heat lost by one part of

the system is equal to the heat gained by another part:

heat lost = heat gainedor

energy out of one part = energy into another part

Calorimetry

If 200 cm3 of tea at 95C is poured into a 150-g glass cup initially at 25C, what will be the common final temperature T of the tea and cup when thermal equilibrium is reached, assuming no heat flows to the surroundings?

Calorimetry

T = 86C

Would this be the case in the “real world”?

Calorimetry The exchange of energy (as shown in the

previous example) is the basis for the technique known as calorimetry.

Calorimetry is the quantitative measurement of heat exchange.

A calorimeter is used.

CalorimetryA simple water calorimeter

Calorimetry

An engineer wishes to determine the specific heat of a new metal alloy. A 0.150-kg sample of the alloy is heated to 540C. It is then quickly placed in 400 g of water at 10.0C, which is contained in a 200-g aluminum calorimeter cup. The final temperature of the system is 30.5C. Calculate the specific heat of the alloy.

Calorimetry

c = 500 Jkg-1C-1

Calorimetry In order to determine the specific heat of a

particular substance, the following expression is used:

Qlost = Qgained

m1c1ΔT1 = m2c2 ΔT2

where the two substances share a final temperature

Thus, all other quantities except one must be measured or known.

Phase change Recall that matter most commonly exists

in three states: solid, liquid, and gas.

What are the differences between these three states (or phases) in terms of molecular structure and motion?

Phase changeComparison of the three common phases of matter (on Earth)

Shape Volume Particle motion

solid

liquid

gas

Phase change

Comparison of the three common phases of matter (on Earth)

Shape Volume Particle motion

solid definite definite vibrational

liquid indefinite definitevibrationalrotational

translational

gas indefinite indefinitesame as liquid

but quicker

Phase change When a material changes phase from

solid to liquid or liquid to gas, a certain amount of energy is involved in this change of phase.

Phase changeTemperature as a function of heat added to 10.0 g of ice

Phase change The heat required to change a substance from

solid to liquid is called latent heat of fusion.

The heat required to change a substance from liquid to gas is called the latent heat of vaporization.

Values for latent heats will vary depending on the substance.

Phase change

Latent heats

Substance Heat of fusion /kJkg-1

Heat of vaporization /

kJkg-1

oxygen 14 210

ethyl alcohol 104 850

water 333 2260

iron 289 6340

Phase change What factors might affect the amount of

energy needed to change the phase of a substance?

Phase change The heat involved in a change of phase Q

depends not only on the latent heat but also on the total mass of the substance, i.e.

Q = mLwhere m is the mass of the substance and L is the latent

heat

Phase change

How much energy does a freezer have to remove from 1.5 kg of water at 20C to make ice at –12C?

Phase change

6.6 x 105 J

Phase change

At a reception, a 0.50-kg chunk of ice at –10C is placed in 3.0 kg of tea at 20C. At what temperature and in what phase will the final mixture be?

The tea can be considered as water. Ignore any heat flow to the surroundings, including the container.

Phase change

T = 5C

Phase change

The specific heat of liquid mercury is 140 Jkg-1C-1. When 1.0 kg of solid mercury at its melting point of –39C is placed in a 0.50-kg aluminum calorimeter filled with 1.2 kg of water at 20.0C, the final temperature of the combination is found to be 16.5C. What is the heat of fusion of mercury in Jkg-1?

Phase change

L = 11 x 103 Jkg-1

Objectives Define specific heat capacity. Solve problems involving specific heat

capacities. Explain the difference between solid, liquid,

and gaseous phases. Explain in terms of molecular behavior why

temperature does not change during a phase change.

Define latent heat. Solve problems involving latent heats.

Measuring specific heat

mass of metalinitial temperature of metalmass of calorimetermass of calorimeter + waterinitial temperature of waterfinal temperature

Data collection

Measuring specific heat

Data processing Include propagation of uncertainty

mass of waterΔT of waterΔT of metal

Measuring specific heat

Data processing Include propagation of uncertainty

Q = mcΔTQ (lost) = Q (gained)

mass of waterΔT of waterΔT of metal

Measuring specific heat Homework

Write a conclusion and evaluation of the lab activity

Design a homemade calorimeter using the materials available. Try to minimize the amount of energy lost to the surroundings.

You will use this calorimeter for the next lab activity. The calorimeter with the smallest percent discrepancy gets bonus points.

Measuring latent heat of fusion

Data collection

mass of cup 1mass of cup 1 + watermass of cup 2mass of cup 2 + iceinitial temperature of iceinitial temperature of waterfinal temperature

Measuring latent heat of fusion

Data processing

mass of waterT of waterΔ

mass of iceT of iceΔ

Measuring latent heat of fusion

HomeworkComplete your data processing.Make sure to include a sample calculation that shows the propagation of uncertainty.Write a conclusion for your data, is the known value for the latent heat of fusion of water within your range of uncertainty?