Physics 161 In Class Lab Exercise 2
Due in Class Friday, May 23, 2003
Part I. Specific Heat Capacity of Materials

Name                                                                  
Date                                                       

Basic idea: A hot object can be used to warm up some cool water by simply dumping it into the water. Since materials differ in their ability to store heat energy on a per unit weight basis, the water will be warmed to different temperatures, depending on how much energy is stored (per unit weight) in the object. We will start with some different metals and other materials all at the same temperature, in a pan of boiling water at
100 degrees C.

We will put the hot object into 200 ml (200 g) of water in a styrofoam cup. The experiment is to allow the two to exchange energy, and measure the final temperature.

From final temperature we can calculate the unknown specific heat capacity of the hot material. Internationally, the specific heat capacity of water is defined to be 1 cal/g/C.

Theory:

The amount of heat Q (in calories) that must added to an object to raise its temperature by T is

Q = Mc delta T

M = mass in grams

c = heat capacity

delta T = temperature change in degrees C (final-initial)= T_f-T_i

If we put a hot metal object (T_m) into cold water T_w, the two will reach a final temperature T_f, which will be somewhere between T_m and T_w.
Using conservation of energy (ignore loss of heat to air and styrofoam cup).

Heat lost by metal = Heat gained by water

-M_m c_m T = M_w c_w T

With a little algebra, you can prove that the heat capacity c_m of the metal (c_w = 1) is

Cm = M_w(T_f -T_w) / M_m(T_m - T_f)

Check that this formula makes sense! If you add 200 g of boiling water to 200 g of water at room temperature, the final temperature (T_f) should be exactly halfway between boiling and room temperature.

IN CLASS

1. Record data obtained in class for three materials of your choice, and for "Object X", some object to be picked and for which we don't know the answer! Use the work sheet below.

Work sheet

AT HOME

2. Calculate the heat capacity of the objects and enter them in the table above.

3. Compare the values you obtain with standard values given (not all are available!):

4. Do at home: Questions for Part I.

1. How well did you do? Did the experiment work (that is, do your results agree with what is accepted?) What would you do to improve the accuracy of the experiment?

2. Which material has the greater heat capacity, (higher specific heat by weight) and how does it compare to the heat capacity of water?

3. Does "object X" behave more like a metal, or water in terms of heat capacity?

4. For some comfort on a cold night, would you take 10 kg of warm rocks, or 10 kg of warm water to bed with you? Explain.

Part 2. Generate Electricity!

Purpose:

The purpose of this part of the lab is to examine the conversion of gravitational potential energy to usable electrical energy. This is model for hydroelectric power generation. The experimental setup consists of a pulley wheel attached to a small generator. A string with a mass attached at one end is wound around the pulley wheel. The falling mass will cause the wheel to turn and generate electricity, lighting up a small bulb. With a current meter (an ammeter) and a voltmeter, we can measure the electric current passing through and the voltage across the bulb. By measuring the current and voltage produced, which yields the electrical power, and the time it takes the mass to fall one meter, you can calculate what fraction of the potential energy of the falling mass is being converted into light and heat energy.

You will need to measure the height h from which the mass falls and use this same height for each measurement.

Equipment:

Generator setup, some masses (0.5, 0.75 and 1.0 kg), meter stick, voltmeter, ammeter, bulb, stopwatch.

PART A:

First connect a light bulb to the leads of the generator and connect one of the masses to the string. Determine and measure the height from which you will drop the mass. Wind up the string and drop the mass a couple of times to observe what happens to the bulb as the mass falls.

h = __________ meters     mass =                                 Kg

Total potential energy (mgh) = ____________________ Joules

where g = acceleration due to gravity.

Drop the mass with the leads disconnected from the light bulb. Does the mass fall faster or slower? Explain your observations.

PART B:

For two different masses, measure the current produced, the voltage across the lamp, and the time it takes for the mass to fall the distance h. Take about three measurements and enter them in the data table below.

V = voltage (in Volts) P = power = V x I (in Watts) I = current (in Amps)

t = time (in seconds) E = energy = P x t (in Joules, remember a joule is a watt-second)

A. mass =                          Kg

CALCULATIONS:

Average Energy: (E = P_average*t_average) =                       Joules

B. Repeat with a different mass. mass =                           Kg

CALCULATIONS:

Average Energy at the bulb (E = P*t)                                  Joules

PART C: Calculate the efficiency of this energy conversion process.

Efficiency = Useful work done / Energy input.

Efficiency of process in Part A:

Energy in = gravitational potential energy = mgh =                     Joules

Energy out = Power x time =                           Joules

Efficiency = (Energy out/Energy in)x100% =                          %

Efficiency of process in Part B:

Energy in = mgh =                                   Joules

Energy out = power x time =                            Joules

Efficiency= (Energy out/Energy in)x100% =                         %

Discussion: Not all of the gravitational potential energy is converted into electrical energy. Discuss with other people where the rest of the energy imparted by the falling mass has gone and write down some of the possibilities below. Is it possible to have an efficiency of 100%? (Think about the falling mass, kinetic energy and the needed speed of the generator to light the light bulb.) Is there a difference for the two masses? If so, why?

Some people have imagined connecting an electrical generator to a motor. The power from the motor would generate electricity that in turn would run the motor. The extra energy could be used to run some lights, a TV, etc. Sounds great, doesn't it! Explain the problem with this idea.