Temperature, Kinetic Theory, and Sound

Please solve the following problems. You must show all work.

1. A diamond has a mass of 56.6 g and the gold ring it is set in has a mass of 125.6 g. How many carbon atoms are there compared to gold atoms?

2. On a warm summer day in California it can get as hot as 115^oF, and on some cold winter days it can get as cold as -20^oF. What are these temperatures in Celsius? 

3. An aluminum sphere is 5.50 cm in radius. What is its volume expansion coefficient if it increases in volume 2.00 cm³ when heated from 100 ^oC to 151 ^oC?

4. Carbon 12 is defined such that 12g is one mole. So if a diamond is 37.5 g, how many moles of carbon are in it? How many molecules of carbon are in it?

5. 400 L of water is at 4 ^oC. If it took a heat 600 seconds to heat this up to 6 ^oC, what is the power rating of the heater?

6. A 95g cup of tea at 85 ^oC is poured into a 1.25 L large tub of water at 30 ^oC . What is the equilibrium temperature?

7. 150 g of ice at -10.5 ^oC is raised to the melting point and then raised to 76.0 ^oC. How much heat is added to the system?

8. A distant star is 7000 K and radiates 1.20 x10²⁷ W. What is the star’s radius? Assume ε = 1.0.