Physics 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 capacity

Specific heat capacities of specific substances

Substance Specific heat capacity, c / Jkg 1 °C -1

900

-

aluminum copper iron or steel lead wood water (ice) water (liquid) water (steam) human body (average) 390 450 130 1700 2100 4186 2010 3470

Specific heat capacity

Q / J

?

?

constant increased ?

m / kg

increased constant increased constant constant

c / Jkg -1 C -1

constant constant constant constant increased

ΔT / °C or °K

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) (b) 720 kJ 7400 kJ

Specific heat capacity

You 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 gained or energy out of one part = energy into another part

Calorimetry

If 200 cm 3 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.

Calorimetry

A 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 -1 C -1

Calorimetry

 In order to determine the specific heat of a particular substance, the following expression is used:

Q lost m 1 c 1 ΔT 1 = Q gained = m 2 c 2 ΔT 2

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 change

Comparison 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)

solid liquid gas Shape

definite indefinite indefinite

Volume

definite definite indefinite

Particle motion

vibrational vibrational rotational translational same 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 change

Temperature 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

oxygen ethyl alcohol water iron

Heat of fusion / kJkg -1

14 104 333 289

Heat of vaporization / kJkg -1

210 850 2260 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 = mL

where 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 10 5 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 -1 C -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 10 3 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

Data collection

mass of metal initial temperature of metal mass of calorimeter mass of calorimeter + water initial temperature of water final temperature

Measuring specific heat

Data processing Include propagation of uncertainty

mass of water ΔT of water ΔT of metal

Measuring specific heat

Data processing Include propagation of uncertainty

mass of water ΔT of water ΔT of metal

Q = mcΔT

Q (lost) = Q (gained)

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 1 mass of cup 1 + water mass of cup 2 mass of cup 2 + ice initial temperature of ice initial temperature of water final temperature

Measuring latent heat of fusion

Data processing

mass of water ΔT of water mass of ice ΔT of ice

Measuring latent heat of fusion

 Homework Complete 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?