1) You have been given the job of finding the specific heat capacity of two materials. You do two experiments, where you have both materials in thermal contact and equilibrium. For the first experiment and for material “Type 1” you have .5 kg, and for material “Type 2” you have .3 kg. In the first experiment, you measure 7.83 x 10⁴ joules lost (take joules lost to be a negative quantity) when the combined materials drop 90 degrees. In the second experiment, you have .2 kg of material 1 and .3 kg of material 2 and measure 2.55 x 10⁴ joules lost when the combined materials drop 50 degrees. What are the specific heat capacities (in SI units please) of the two materials? Assume that no phase change has taken place.

2) You have measured the total heat lost during cooling of a lava lake and it is 4.8 x 10¹² joules. The volume of the lava lake is 1000 cubic meters, and the density (assumed constant for this problem) is 3200 kg/m³. The temperature drop from liquidus to complete cooling was 1200 degrees. Assume that the value of the specific heat capacity for lava is 1000 (J/kg*K). What percentage of the total heat is due to the latent heat of crystallization? What is the value of the specific latent heat (J/kg)?

3) You have a cup of coffee with volume .0003 m³ that is initially 80⁰ and you bring it into a room that is that we will assume is held at 20⁰. The density of the coffee is 1000 (kg/m³) and the specific heat is 4184 (J/kg*K). What is the total amount of thermal energy (relative to the room temperature) in the coffee? Now if the cup of coffee loses heat at a constant rate of -20 (J/s), plot how the temperature of the coffee changes with time (assume that the coffee is well stirred and that once it hits room temp, the cooling stops). How long will it take to reach room temperature? How good was our assumption that the room was held at constant temperature during this process- assume that the room has a well mixed volume of 3 m x 3 m x 3 m, and that the density of air is 1.2 (kg/m³) and that the specific heat capacity of air is 1000 (J/kg*K).

4) Now instead of a coffee cup, assume that we have a popsicle at -10⁰. It has the same mass as the coffee. Given the same heat transfer rate (except this time it is heating up) how long will it take before it starts to melt? How long before it is all melted? How long before it comes to room temperature? Plot the temperature of the popsicle vs. time on the same plot as you made for the coffee. The specific heat for the popsicle while it is solid is 2108 (J/kg*K), and while liquid use the same value as the coffee. The latent heat is 3.34x105 (J/kg).

5) How many 75 Watt light bulbs could you light if you could gather all the geothermal energy coming out of 5 square kilometers of continental crust?

6) If radioactive decay is an important source of energy to power plate tectonics, are rates of plate motion speeding up, slowing down, staying constant? Why?

7) If the crust is 30 km thick, and the thermal conductivity is 2.5 (W/m*K) and the temperature at the Moho is 950 degrees C, what is the heat flow at the surface?

1) You have been given the job of finding the specific heat capacit...