Week 22 (Jan. 19 - 23)
Reading: Heat engines, Entropy, and the second law (Chap. 22)
Key Topics: the first and second laws of thermodynamics, specific heat capacity, latent heat, calorimetry, entropy, disorder,
Key Topics: the first and second laws of thermodynamics, specific heat capacity, latent heat, calorimetry, entropy, disorder,
Week 22 Homework Problems:
- Heat conduction: The right end of a bar of gold is in thermal contact with the left end of a bar of silver of the same length and cross-sectional area. The left end of the gold bar is maintained at 80.0 deg. C; the right end of the silver bar at 30.0 deg. C. When the system reaches steady-state, what is the temperature at the junction of the bars?
- Two light bulbs are identical except that one has a filament that operates at 2500 K, while the other operates at 2200 K. Find the ratio of the power radiated by the hotter one to the power radiated by the cooler one.
- Melting an ice cube: How much heat is required to vaporize a 1.0 kg ice cube initially at 0 deg. C? The latent heat of fusion of ice is 80 cal/gram and the latent heat of water is 540 cal/gram.
- Calorimetry: Suppose that one pound of pasta (spaghetti, let's say) at room temperature is dumped into one gallon of boiling water. How much does the temperature of the water drop by the time the pasta comes into thermal equilibrium with the water? Assume that the water is not on the stove (so no additional heat is being added to the water). Hint: look up the specific heat of pasta/flour.
- Find the change in entropy that results when a 2.3 kg block of ice melts slowly (reversibly) at 273 K (0 deg. C).
- Entropy Challenge problem: A 1 gram block of copper initially at 100 deg. C is placed gently into an insulated cup containing 10 grams of water initially at 20 deg. C. When thermal equilibrium is finally reached, (i) what is the temperature of the water and the block? (ii) what is the change in entropy of the water? of the block? (Hint: since the temperature of each object is changing as heat leaves (or enters) the object, you will need to integrate dQ/T from T_init to T_final to get each object's change in entropy. When doing each integral, use the fact that dQ = mcdT). (iii) Did the total energy of the system (block + water) increase, decrease or remain the same? (iii) Did the total entropy of the system increase, decrease, or remain the same?
