Laboratory

Report

Submitted to: Mabel Yacon

Submitted by: Marc Terence Novera

Date: January 6, 2014

I. Objectives Determining the temperature of water before mixing, and after mixing.

II. Theory

Heat capacity, or thermal capacity, is the measurable physical quantity of heat energy required to change the temperature of an object or body by a given amount. The SI unit of heat capacity is joule per kelvin, and the dimensional form is M1L2T−2Θ−1.

Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. When expressing the same phenomenon as an intensive property, the heat capacity is divided by

the amount of substance, mass, or volume, so that the quantity is independent of the size or extent of the sample. The molar heat capacity is the heat capacity per mole of a pure substance and the specific heat capacity, often simply called specific heat, is the heat capacity per unit mass of a material. Occasionally, in engineering contexts, the volumetric heat capacity is used.

Temperature reflects the average randomized kinetic energy of particles in matter, while heat is the transfer of thermal energy across a system boundary into the body or from the body to the environment. Translation, rotation, and a combination of the two types of energy in vibration (kinetic and potential) of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of matter, but loosely bound electrons may also participate. On a microscopic scale, each system particle absorbs thermal energy among the few degrees of freedom available to it, and at sufficient temperatures, this process contributes to the specific heat capacity that classically approaches a value per mole of particles that is set by the Dulong-Petit law. This limit, which is about 25 joules per kelvin for each mole of atoms, is achieved by many solid substances at room temperature.

The heat capacity of most systems is not a constant. Rather, it depends on the state variables of the thermodynamic system under study. In particular it is dependent on temperature itself, as well as on the pressure and the volume of the system.

Different measurements of heat capacity can therefore be performed, most commonly either at constant pressure or at constant volume. The values thus measured are usually sub scripted (by p and V, respectively) to indicate the definition. Gases and liquids are typically also measured at constant volume. Measurements under constant pressure produce larger values than those at constant volume because the constant pressure values also include heat energy that is used to do work to expand the substance against the constant pressure as its temperature increases. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.[citation needed]

The specific heat capacities of substances comprising molecules (as distinct from monatomic gases) are not fixed constants and vary somewhat depending on temperature. Accordingly, the temperature at which the measurement is made is usually also specified. Examples of two common

ways to cite the specific heat of a substance are as follows:[4]

Water (liquid): cp = 4.1855 [J/(g·K)] (15 °C, 101.325 kPa) or 1 calorie/gram °C

Water (liquid): CvH = 74.539 J/(mol·K) (25 °C)

For liquids and gases, it is important to know the pressure to which given heat-capacity data refer. Most published data are given for standard pressure. However, quite different standard conditions for temperature and pressure have been defined by different organizations. The International Union of Pure and Applied Chemistry (IUPAC) changed its recommendation from one atmosphere to the round value 100 kPa (≈750.062 Torr).[notes 1]

Measuring the heat capacity, sometimes referred to as specific heat, at constant volume can be prohibitively difficult for liquids and solids. That is, small temperature changes typically require large pressures to maintain a liquid or solid at constant volume implying the containing vessel must be nearly rigid or at least very strong (see coefficient of thermal expansion and compressibility)

For any given substance, the heat capacity of a body is directly proportional to the amount of substance it contains (measured in terms of mass or moles or volume). Doubling the amount of substance in a body doubles its heat capacity, etc.

However, when this effect has been corrected for, by dividing the heat capacity by the quantity of substance in a body, the resulting specific heat capacity is a function of the structure of the substance itself. In particular, it depends on the number of degrees of freedom that are available to the particles in the substance, each of which type of freedom allows substance particles to store energy. The translational kinetic energy of substance particles is only one of the many possible degrees of freedom which manifests as temperature change, and thus the larger the number of degrees of freedom available to the particles of a substance other than translational kinetic energy, the larger will be the specific heat capacity for the substance. For example, rotational kinetic energy of gas molecules stores heat energy in a way that increases heat capacity, since this energy does not contribute to temperature.

In addition, quantum effects require that whenever energy be stored in any mechanism associated with a bound system which confers a degree of freedom, it must be stored in certain minimal-sized

deposits (quanta) of energy, or else not stored at all. Such effects limit the full ability of some degrees of freedom to store energy when their lowest energy storage quantum amount is not easily supplied at the average energy of particles at a given temperature. In general, for this reason, specific heat capacities tend to fall at lower temperatures where the average thermal energy available to each particle degree of freedom is smaller, and thermal energy storage begins to be limited by these quantum effects. Due to this process, as temperature falls toward absolute zero, so also does heat capacity.

http://en.wikipedia.org/wiki/Heat_capacity

III. Summary of the Procedure

Here are the materials we used in the experiment.

Heat source (Bunsen burner, alcohol burner, or hot plate)

Tripod Wire gauze 500 mL beaker Two identical plastic beakers Two metal specimens (Copper and Iron)

Platform balance Thermometer Two pairs of tongs 500 mL of water

Procedure:

We weigh the metal specimens using the platform balance. Then boil 300 mL of water in the 500 mL beaker and then place the two metal specimens into the boiling water for around 10 minutes. The two specimens will eventually have the same temperature as the water (assumed to be 100 Celsius). Then fill each of the plastic beakers with 100 mL of water at room temperature. Label the beakers Specimen 1 and Specimen 2. Measured and recorded the temperature of the water from each beaker. Using the tongs, we quickly but carefully place the metal specimens separately into the plastic beakers. Measuring and recording the final temperature of water in the plastic beakers. Then after it’s done we record it on the data table.

IV. Data and Result

Ti Tf m C

H20 29°C 30°C 0.1392 kg 4190 J/kgMetal 1 (Iron)

100°C 30°C 0.0008 kg 10,415.14 J/kg

Ti Tf m CH20 29°C 31°C 0.1392 kg 4190 J/kg

Metal 2 (Copper)

100°C 31°C 0.008 kg 2,113.22 J/kg

Metal 1 (Iron)

Given: H20: m = 0.1392 kg Heat gained H20 = mc(ΔT)

C = 4190 J/kg = (0.1392 kg)(4190 J/kg)(1 C)

Tf = 30 C = 583.248 J

Ti = 29 C

ΔT = 1 C

Metal 1: m = (0.0008 kg) Heat lost metal = mc ΔT

Tf = 30 c = (0.0008 kg)(c)(-70 C)

Ti = 100 C = -0.056 kg c c

ΔT = -70 C heat gained + heat lost = 0

(583.248) + (-0.056 kg°c °c) = 0

583.248 J0.056kgc = 0.056kgc0.056kgc

= 10,415.14 J/kg °C = °C

% error = standard value−experimental valuestandard valie x 100

% error = 470

Jkg

−10,415.14 J /kg

470 J / kg x 100

% error = −9,945.14 J /kg470 J /kg x 100

= 121.6 %

Metal 2: m = 0.1392 kg Heat lost metal = mc ΔT

Given: H20 Tf = 31 °C = (0.0008 kg)(c)(-69 C)

Ti = 29 °C = -0.0552 kg °c °c

ΔT = 2 °C

Metal (Copper)

M = 0.0008 kg ΔT = 69 °C

Tf = 31 °C

Ti = 100 °C

heat gained + heat lost = 0

(1166..4965) + (-0.0552 kg°c °c) = 0

1166.496J0.0552 = 0.05520.0552

= 2,113.22 J/kg °C = °C

% error = standard value−experimental valuestandard valie x 100

% error = 390

Jkg

−2,113.22J /kg

390 J /kg x 100

% error = −9,945.14 J /kg470 J /kg x 100

= -441.85 %

V. Setup

VI. Discussion

The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. The relationship between heat and temperature change is usually expressed in the form shown below where c is the specific heat. The relationship does not apply if a phase change is encountered, because the heat added or removed during a phase change does not change the temperature.

The specific heat of water is 1 calorie/gram °C = 4.186 joule/gram °C

which is higher than any other common substance. As a result, water plays a very important role in temperature regulation. The specific heat per gram for water is much higher than that for a metal, as described in the water-metal example. For most purposes, it is more meaningful to compare the molar specific heats of substances.

VI. Conclusion

The higher the specific heat of an object, the higher the thermal energy needed to be transferred to the object to raise its temperature.