1. What is the temperature in degrees Celsius when the Fahrenheit temperature is 60 oF?
2. What is the temperature in degrees Kelvin when the Fahrenheit temperature is 85 oF?
3. By how much does the temperature in degrees Celsius change when the temperature in degrees Fahrenheit changes by 10 Fo?
4. By how much does the temperature in Kelvin change when the temperature in degrees Celsius changes by 10 Co?
5. At what temperature do the Fahrenheit and Celsius scales have the same reading?
6. At what temperature do the Kelvin and Celsius scales have the same reading?
7. An aluminum rod of length 5.700 cm at 0 oC is dropped into a pot of boiling water (100 oC). What is the length of the rod after it reaches equilibrium with the water?
8. An ideal gas fills a container of volume 0.00047 m3 at a temperature of 290 K. The pressure inside the container is 0.6 patm. How many molecules are in the gas?
9. What kind of process takes place if you slowly compress a gas inside a container which is immersed in a large, warm-water bath which is kept at 38 oC? Why?
10. A piston consists of an upright cylinder with a top which can slide frictionlessly up and down inside the cylinder despite the fact that it makes a tight fit with the cylinder walls (so no gas can leak out; this is just like the picture for problem 18 below, but with no water on top). Two moles of an ideal gas are confined inside the cylindrical piston at room temperature. The piston is then placed on a burner which raises the temperature of the gas to 350 K. What kind of process takes place? Why? Would the piston rise or fall?
II. Some Standards
11. A 3-liter steel container is fitted with an air-tight lid. The container is sitting initially open on a table-top in your lab. The lid is then placed on the container and tightly closed. The entire container is then completely submerged in a large tub of boiling water (100 oC). Estimate the pressure in the container after the container has reached thermal equilibrium with the boiling water. Express your answer in atmospheres. (What kind of process is this?)
12. A very precise aluminum ruler (a = 24 x 10 – 6 1/Co ) is designed to measure the proper length at 22 oC (room temperature). The diameter of a quarter is measured to be 2.495 cm at room temperature. The ruler is then submerged in liquid nitrogen at 77 K and allowed to come to thermodynamic equilibrium. If the ruler is quickly removed from the liquid nitrogen and the diameter of the quarter (still at room temperature) is once again measured, what will be the new ruler reading? (Hint: Should the new reading be larger or smaller? Be careful!)
13. A “precision” aluminum measuring tape measures the length of a stone carving in the middle of the desert to be 269.36 cm when the temperature is 42.6 oC. If the tape was manufactured to be accurate at 20.0 oC, what is the actual length of the carving?
14. An aluminum cylinder has a length of 5.7000 cm and a radius of 1.5000 cm at a temperature of 0.0 oC. (a) What is the length of the cylinder at the temperature of 90.0 oC? (b) What is the change in volume of the cylinder corresponding to this change in temperature?
15. An ordinary ice-cube tray which makes rectangular-shaped ice cubes is sitting in the freezer. One of the ice cubes is missing, and its space in the tray is sitting there empty – that is, empty except for the air which occupies the space that should have been filled with freezing water. Estimate the order-of-magnitude of the number of air molecules that occupies this space for a single ice cube. Clearly state all of your approximations and reasoning.
III. So, you think you’re pretty good...?
16. A long, vertical glass tube has an inner cross-sectional area equal to 
0.030 cm2 and is sealed off at its lower end. A drop of mercury is placed in the opening at the top of the tube at room temperature and pressure. The drop slides freely down the narrow tube until it reaches equilibrium at a certain height above the closed end of the tube. The drop of mercury therefore effectively seals off a certain amount of air. The tube and mercury are then placed in a chamber and heated to 90 oC at atmospheric pressure. (Assume none of the mercury evaporates or is lost to the sides of the tube.) The mercury drop is found to be 75 cm above the closed end of the tube. The tube and gas are then cooled down to 15 oC. (a) Approximately how many air molecules are enclosed by the drop of mercury? (b) What is the final height of the drop of mercury above the bottom of the tube after it reaches equilibrium at 15 oC?
17. A steel automobile fuel tank is filled to the brim with gasoline at 10 oC. The volume of the tank is 45 liters ( 0.04500 m3). Immediately afterward the vehicle is parked in the sun where the temperature becomes 35 oC. How much gasoline overflows from the tank as a result of thermal expansion? bgasoline = 9.6 x 10 – 4 1/Co .
18. A piston of negligible mass can slide freely inside a large cylindrical tank 
of height H = 2.65 m and cross-sectional area A = 0.090 m2. The volume in the cylinder below the piston is filled with air, while the volume above the piston is filled to the brim with water. The piston is then measured to be a distance H/3 below the top of the tank. (Assume the entire system is in thermal equilibrium at room temperature.) Find the number of air molecules inside the cylinder below the piston. (Hint: Draw a FBD for the piston.)
Answers