22SP_PH122L1-General Physics II Lab

In the first part of this lab, we are going to explore what the terms “heat,” “hot,” “cold,” and “temperature” really mean.  What do we mean when we say it is cold outside, or that water is hot? 

In the second part of the lab, we will actually be measuring the temperature of different objects, but what are we really measuring?  A thermometer only tells you the temperature of itself.  We just know that from experience, if we leave the thermometer in our mouth long enough, it will be at the same temperature as our mouth.  We do this so that our mouth and the thermometer are in thermal equilibrium.  So we are going to mix hot water with cold water, in varying ratios, and try to determine a formula that allows us to predict what the final temperature of the mixture will be.

 In the final part of the lab, we will repeat what we did in the second part, but this time the cold water will also contain ice.  Your goal is to find out if using water with ice in it follows the same prediction as using water without ice in it.

You are going to explore how the volume of a gas changes when temperature is kept constant and pressure is varied.  The gas to be studied is a small pocket of air trapped in a glass capillary tube by a column of mercury.  The trapped gas presses outward on the mercury while the air in the room presses inward on it.  The capillary tube is mounted on a ring stand and can be rotated to vary the pressure exerted on it by the mercury column.  As that happens, everything rapidly equilibrates to the ambient room temperature, so temperature remains essentially constant.

Your goal is to determine the pressure inside the air column as its orientation is varied and compare the resulting change in its pressure to the change in its volume.  When the open end of the capillary tube is upward the pressure on the confined air is just the sum of the ambient air pressure above the mercury column and the pressure caused by the entire weight of the mercury column.  From this we can make generalizations about what happens at other angles. To do so, construct a free-body diagram for the column of mercury, then write out Newton’s second law and relate all the forces acting on it.  Do this first for a perfectly upright tube, then generalize to an angled tube, as illustrated above.  You will need the density of mercury, ρ = 13.6 g/cm³, and the day’s atmospheric pressure, which the instructor will write on the board for you to use.

A heat engine is a device that does work by extracting thermal energy from a hot reservoir and exhausting thermal energy to a cold reservoir. In this experiment, the heat engine consists of air inside a cylinder that expands when the attached can is immersed in hot water.  The expanding air pushes on a piston and does work by lifting a weight. The heat engine cycle is completed by immersing the can in cold water, which returns the air pressure and volume to the starting values.

The whole concept of electric potential is very subtle and can be confusing. It is best explained by making an analogy with gravity. Imagine your 1kg textbook sitting on the lab table. That book is approximately 1 meter above the floor, so using Ug = mgh we could calculate its gravitational potential energy relative to the floor as 10 J. The gravitational potential (not energy!) where the book is located is defined as the gravitational potential energy divided by its mass, 10 J/kg. 

We can now repeat that process with a rather rotund person of mass 250 kg. If this person stands on the same table, again approximately 1 meter above the floor, their potential energy relative to the floor is mgh = 2500 J. Dividing their potential energy by their mass again results in a potential of 10 J/kg. That number maintains a consistent value regardless of the mass considered, so it depends on location and not on the mass on the table. 

This shows that anything you put atop the table will have 10 Joules of potential energy for every kilogram of mass it has. To describe this we say that the surface of the table has a gravitational potential of 10 J/kg relative to the floor. This illustrates a very important point: Potential energy is a property of a specific object with a well-defined mass in a particular location, while potential itself is a property of just the location. Nothing need be there for potential to be defined.

To relate this to electricity, we simply need to know that when there is a separation of charge, such as what a battery creates, an electric field is produced that applies forces to any nearby charges. The field lines associated with this field starts on the positive charge and ends on the negative charge. In the same way that we defined gravitational potential as giving the energy per kilogram needed to move in the presence of a gravitational field, electric potential is the energy per change needed to move in the presence of an electric field. Electric potential here is just like the gravitational example above, except its unit is joules per coulomb (J/C) instead of joules per kilogram (J/kg). The unit joule per coulomb is important enough to have its own name: 1 J/C = 1 volt (V). Confusingly, the symbol for electric potential is the same letter but italicized (V).

In an ideal world when charge moves through a wire (or any other conductor), it would move through that wire freely, meeting no resistance or friction.  As you know, the lab is far from an ideal world.  The good news is that we can take advantage of that, and even measure it.  In this lab, you will use an electric field produced by a battery to cause charges to move in a current through a wire.  Those charges will lose energy to friction-like effects (called “resistance”), and that energy will be turned into heat, which will be absorbed by a cup of water.  Knowing the mass and temperature change of the water, you can calculate how much water the energy gains and compare that to how much energy the charges lost.  That is the goal of today’s experiments.

Theoretical background:  Here is a quick overview of the relevant ideas regarding electricity.

·   When a particle with electrical charge q moves along a wire and passes though a potential drop ΔV, its electric potential energy decreases by an amount ΔU_E = q ΔV.  Potential difference ΔV is measured in volts (V), and 1V = 1 J/C.  Of course, charge is in coulombs (C) and energy is in units of joules (J). 

·    Electrical current is the rate at which a net amount of positive charge passes along some path.  In typical conductors, current is actually carried by negatively charged electrons moving in the opposite direction.  However, the effect is identical, and we sometimes refer to the effective movement of positive charge as the conventional current.  For a given amount of time Δt, the current I determines the total quantity of charge q that passes a point in the conductor by q = I Δt.  Current is measured in amperes (A), where 1 A = 1 C/s. 

·    Power is the rate of energy dissipation and is measured in watts (W), where 1W = 1J/s.

Putting these ideas together gives the relation between power dissipated, current, and potential difference.  You must find that relation before starting your experiment!  

You’ll also need to use what you know about how temperature changes when energy is added.  The relation is fairly simple and we will explore it in depth later in the semester:

Q = mcΔT

Here, Q is an amount of energy added to the water, which is provided in this experiment by the charged particles falling through a potential difference, gaining kinetic energy, then giving that energy up via collisions in the metal conductor.  The measured temperature changes by ΔT, and c is a constant that depends on the material in question, which is water in this situation.

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