# University of California, San Diego Physics 1b - Thermodynamics, Electricity & Magnetism

 H. E. Smith Spring 2000

 Physics 1B - Tutorial #1

1. What temperature has the same numerical value in Celsius (Centigrade) and Fahrenheit? Is there a temperature which has the same value on the Celsius and Kelvin (thermodynamic) scales?
2. A circular iron plate has a coefficient of linear expansion of 10-5K-1. At 20C it has a central circular hole of radius 2 inches. The plate is then heated to 40C.
• Does the size of the hole increase, decrease or remain the same?
• Calculate the numerical value of the radius at 40C.
3. The surface area of the earth is approximately 5 x 1014m2. The scale height (thickness) of the earth's atmosphere is 104m. A cubic meter of air at room temperature and a pressure, P = 1 atmosphere, has a mass of 1.3kg.
• Estimate the mass of air on the earth.
• A mole of air has a mass of 0.029kg (Why?). How many molecules does the earth's atmosphere contain?
• Assuming that the atmosphere has become completely mixed over the last 2000 years, how many molecules from Julius Ceasar's last breath are in your lungs at the current moment.
4. You use superglue to attach a strip of copper to a strip of aluminum at 20C. Coefficients of linear expansion: Cu = 16.6 x 10-6K-1; Al = 25 x 10-6K-1.
• What will happen if you heat the strips to 40C? Make a sketch.
• What will happen if you cool the strips to 0C? Make a sketch.
• How will the behaviour of the strips depend upon thickness: i.e. if they are very thick (like metal bars) or very thin (like paper strips).
• Can you think of practical uses of devices employing this behaviour?
• For a device made of two metal strips such as this one, what parameters are important in determining how the strips bend? Which would make bending larger? Which would make bending smaller? (Consider the coefficients of linear expansion, initial & final temperatures, strip length & thickness, anything else that you think might be important.
• (OPTIONAL) Suggest a formula to describe the bending using the parameters discussed above in (e).
5. As you learned in Physics 1A, rocket propulsion employs the principle of Conservation of Linear Momentum. Ideally, the burning (oxidation) of hydrocarbon fuels produces water (H2O) and carbon dioxide (CO2) which are expelled at high velocity. Sketch a diagram of how the burning of rocket fuel propels a rocket forward.
• A rocket of mass 1 metric ton (1000 kg) expels CO2 with an exhaust speed of 1000m/s. How much CO2 must be ejected to accelerate the rocket by 1000 m/s.
• Compare the rms speeds of water and carbon dioxide at a temperature of 1000 K. Does the rms speed depend upon the pressure?
• Use a balloon to demonstrate rocket propulsion. What is the typical speed of the escaping molecules? Do they carry away momentum?
6. The next time you are home, take apart your thermostat and demonstrate to your parents how a bi-metallic strip works. Four brownie points if you can reassemble the thermostat and your home heating system still works,

Gene Smith