PHYSICS 123 EXPERIMENT NO. 10

THE MECHANICAL EQUIVALENT OF HEAT

Historically, the relationship between heat flow into a material and its resulting temperature change was deduced prior to mankind’s understanding of heat as a form of energy. A unit of heat (the calorie) was invented to quantify heat flow. A calorie is defined as that amount of heat necessary to raise one gram of water by one degree Celsius.

The equivalence of heat energy and mechanical energy was deduced by measuring the amount heat created when an object undergoes a known amount of work due to a non-conservative force. We will use this technique to measure the proportionality constant between the old heat unit (the calorie) and the MKS energy unit (the Joule).

A.Equipment

1spring balance

1thermometer

1stirring rod

1inner brass cup

1outer brass cup

1small clamp (check limitation of screw)

1large C-clamp

1pliers to tighten clamp

1 crank with gears , turning black cylinder

B.Method

A schematic diagram of the apparatus is shown below. The inner brass cup is partly filled with water. The outer brass cup is connected to a crank handle and turned about the axis of rotation shown. The inner cup is stationary. Thus, with the inner cup lowered into the outer cup, there is friction. The work done by the frictional force is converted to heat. The mechanical work done (in Joules) and the heat generated (in calories) are measured and thus the conversion factor between the 2 units determined.

Since the inner cup is in equilibrium, the torque due to friction is balanced by the torque due to the external force applied to the edge of the aluminum disk. Since work is equal to torque * angle, we find (W=*):

W = FR 2N = 2R FN (1)

where R is the radius of the disk, F is the force applied to keep the inner cup stationary, and N is the number of turns of the outer cup.

We can analyze the amount of heat input to the system by measuring the change in temperature. In general, Q = mcT for a single material which does not undergo a phase change. In our case, several pieces of the apparatus are heated at the same time. The total heat input is:

Q = mwcwT + mbcbT + mscsT + mthcthT (2)

where w represents the water, b the brass pieces, s the stir rod, and th the thermometer. Using the known specific heats of each substance (in Calories/kg*K), we can determine the heat flow in calories and compare this result to the work done (in Joules).

C.Procedure

1.Disassemble the apparatus and measure the mass of each relevant part. The mass of the water can be deduced by weighing the inner cup with and without the water.

2.Reassemble the device with the inner cup 3/4 filled with cold water (roughly 6-8° C below room temperature). Stir the water and measure the starting temperature. Place a scrap of paper between the inner and outer cup during reassembly so that the crank will turn smoothly.

3.The crank handle is attached to a counter so that the number of turns can be measured. Record the starting value of the counter and begin to crank.

4.The force necessary to keep the inner cup stationary is read from a spring balance. Record its value. Try to keep the force steady by turning the crank very smoothly and continuously.

5.While one partner cranks, the other should record the temperature of the water approximately every minute. DO NOT Stop cranking the device during these “spot-check” temperature measurements. If fatigue should set in, the lab partners should switch jobs.

6.Continue to crank the apparatus until the final temperature is roughly as far above room temp as the initial T was below it. After cranking is finished, record the new reading on the counter.

7.Take several temperature measurements every minute even after the cranking is finished since the T value will continue to rise for a short time.

8.Calculate the the work in Joules from equation (1) and the heat in calories from equation (2). Determine the ratio, W/Q and compare it to the accepted value. (4.187 Joules/Calorie)

Q1.Why is it best to start the experiment below room temp and end above?

Q2.Why is it necessary to stir the water before each temperature measurement?

Q3.Why is there a residual upward drift in temperature after the cranking is stopped?

Q4.It takes about 100,000 Joules to toast bread. Compare this amount to the mechanical work you did during the experiment.

What you need:

  1. Mass of each relevant part
  2. Starting value of the counter
  3. Ending value of the counter
  4. Value of the force
  5. Starting temperature value
  6. Temperature values at approximately each minute
  7. Calculation of the work
  8. Calculation of the heat
  9. Calculation of the ratio
  10. Comparison to known value
  11. Answers to 4 questions