IN ALL PROBLEMS USE g = 10m/s^2 for simpler calculations unless stated otherwise in the problem.

PLEASE be careful with keeping units consistent with other units and do not mix units from SI and CGS systems, i.e, cm and kg. Please be sure to include units in your answer as some of the answers will be very sensitive to the unit they are attach to. 

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? Notes***  Assume the tea is water as far as specific heat input for tea. Because the tea is assumed as water assume 1.25L = 1.25kg for mass of water. Write out the heat lost = heat gained

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.

PLEASE be careful with keeping units consistent with other units and please do not mix units from SI and CGS systems, i.e, cm and kg. Please be sure to include units in your answer as some of the answers will be very sensitive to the unit they are attach to.