## Activity Based Physics Thinking Problems in Thermodynamics: Temperature

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### Activity Based Physics Thinking Problems in Thermodynamics: Temperature

 1) An open gas cylinder filled with air is fitted with a smoothly fitting piston. The piston is lubricated with a wax that allows the piston to slide, but does not permit any air to escape around the piston. The entire system is placed in a vacuum, and the piston allowed to settle. It comes to rest in the position shown. The mass of the piston is m, the temperature of the system (in degrees Celsius) is T, the circular area of the piston is A, and the gas in the cylinder contains N molecules. a) Find the height of the piston above the bottom of the cylinder in terms of the givens and any fixed constants you may need. Now suppose the position of the piston is fixed by a pair of pins (shown), and an equal amount of gas (at the same temperature) is introduced into the cylinder through a valve at the back (not shown). b) How does the force that the gas exerts on the piston change? (Be quantitative - for example, say "drops by 25%" instead of "decreases".) c)How does the average speed of a molecule in the gas change? (ditto)

2) A 500 g piece of copper is accidentally dropped into liquid nitrogen (T = -180 oC). In order to warm up the copper, a student removes it from the nitrogen and immediately places it in a Styrofoam cup containing 400 g of water. The water is at a temperature of 15 oC. Predict the final equilibrium state that is attained within the Styrofoam cup. Explain your reasoning and interpret, in words, the physical meaning of each separate term that is present in any equation you use. Some of the following constants may be of use: cwater = 1.0 cal/g oC; cice = 0.49 cal/g oC; ccopper = 0.092 cal/g oC; Lf,water = 80 cal/g; Lf,copper = 49 cal/g; k = 1.38 x 10-23 J/ oC 1 cal = 4.186 J

3) An experiment on the melting of ice is being done in an insulated calorimeter set up so no heat is exchanged with the outside environment. The calorimeter contains a mass m1 of water and a block of ice having a mass m2, is floating in the water. Both the ice and the water are at a temperature of 0 oC.

(a) What mass of boiling water, m3, must be added to the system to produce only water at 0 oC? Express your answer in terms of symbols, defining symbols for any heat capacities you require.
(b) Suppose m1 = 100 grams, m2 = 25 grams, and I add 50 grams of boiling water. When the system comes to thermal equilibrium, will there be any ice left? If there is none, what will the final temperature of the water be? The following numbers may be of some use: 1 cal/gram-oC 80 cal/gram 540 cal/gram

4) For each of the following partial sentences, indicate whether they are correctly completed by the symbol corresponding to the phrase greater than (>), less than (<), or the same as (=).

(a) A chunk of iron is heated to a temperature of 120 oC. It is then moved into a container of water at room temperature. The water in the container has the same mass as the iron. The change in the water's temperature due to the insertion of the iron will be __________ the change of the iron's temperature due to its insertion into the water.
(b) A chunk of iron is heated to a temperature of 120 oC. It is then placed into a hole prepared for it in a large block of ice. After a period of time, the ice stops melting and the iron is sitting in a pool of water melted out of the ice. The pool sits in a depression in the remaining ice which it has melted out. The temperature of the water in that pool is __________ 0 oC.
(c) A chunk of iron is sitting on a scale. It is then covered by a bell jar which is air-tight and which has a nozzle connected to a vacuum pump. When the air is pumped out of the bell jar, the scale reading will be __________ it was when there was air. (Assume the scale would read zero if nothing were sitting on it, even when the air is pumped out.)
(d) A chunk of iron is sitting on a scale. The iron and the scale are then both immersed in a large vat of water. After being immersed in the water, the scale reading will be __________the scale reading when they were simply sitting in the air. (Assume the scale would read zero if nothing were sitting on it, even when it is under water.)

5) Three important concepts in the study of thermodynamics are, temperature, heat, and internal energy. Discuss the meaning of these three concepts being careful to distinguish between them.

6) I have two beakers of water. Each holds one kg of water. One is sitting at room temperature (25 °C). The other is sitting on a hot plate and is boiling. I place a block of iron with a mass of 0.2 kg into the boiling water and leave it until the water starts boiling again. I then remove it from the boiling water and place it into the other beaker. If the specific heat of iron is 0.12 Cal/(kg-°C) what will be the final temperature of the water and iron once they come to thermal equilibrium?

7) At time t=0 a hot object at a temperature T1 is placed in an environment at a temperature T0. The temperature of the object will be some function of time, T(t). This function will satisfy the equation:

(a) Explain what this equation is telling you in words.
(b) Show that the function satisfies the equation above.
(c) Find the value of the constant c for the particular case we are considering.

These problems written and collected by E. F. Redish. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity Based Physics Thermodynamics Problems site is mentioned and the URL given. Web page created and edited by K. A. Vick.

To contribute problems to this site, send them to redish@physics.umd.edu.

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Comments and questions may be directed to E. F. Redish