# Thermodynamics

#### Thermal Expansion

1. The Empire State Building is 443m tall lets say when it is 15ºC outside. If it is primarily steel (coefficient of linear expansion $\alpha = 13 \times 10^{-6}$ /ºC), how much taller will the building be in the summer when it is 40ºC?
2. The Statue of Liberty is 46m tall lets say at 20ºC.  It is made out of copper (coefficient of linear expansion $\alpha = 17 \times 10^{-6}$ /ºC).  How much shorter is it when the temperature falls to -30ºC?

#### Ideal Gas Law

1. If you had a ballon filled with air at sea level (P = 1 atm, ρ = 1.2 kg/m³, T = 25ºC) that has a radius of 1.5m, what radius would it have if submerged 30m below the water if the temperature remains unchanged?
2. A hot air ballon works by heating the air in a ballon so that it has a lower density than the air outside.  The volume of a ballon is 4.0m³ before it is heated. If the air in athe ballon is heated from 25ºC to 55ºC while the pressure remains the same as the air outside, what will be the volume of the ballon after this change? What buoyant force would this provide?
3. If your bike has a flat tire where its pressure is 300000Pa when it should be 700000Pa if fully inflated.  The volume of the tire is 1.5L.  By what amount must you increase the amount of air in the tire to get to the desired pressure assuming no change in temperature?
4. A zeppelin is an airship that stays afloat by being filled with hydrogen.  If a zeppelin has a mass of 15000kg and the density of air is 1.2 kg/m³, what volume must the zeppelin have to float in the air?  If the temperature of the hydrogen in the zeppelin was 25ºC and it was increased to 50ºC what would this do to the zeppelin’s volume if the pressure stayed the same?
5. What is the rms speed of molecules in a helium ballon which is at 25ºC?
6. What is the rms speed of water vapor molecules that are at 100ºC?

#### Heat Energy

1. The rubber steering wheel of a car has a mass of 0.50kg and a heat capacity of cv = 2000 J/kg ºC. Leaving it in the sun the temperature of the wheel goes from 25ºC to 40ºC. How much energy has the steering wheel absorbed?
2. A cup of tea with volume 60.0cm³ at a temperature 85ºC cools to 25ºC. How much energy is lost by the tea?
3. 100mL of coffee at 90ºC is poured into a 0.50kg porcelain cup (cv = 1100 J/kg ºC) which is initially at 20ºC. What equilibrium temperature will the coffee and cup come to if no heat is lost?
4. A long time ago hot baths were sometimes made by dropping hot stones into a tub of water.  If one had a tub with 1.50m³ of water in it at 20ºC and one added 2.5kg of stone (cv = 790 J/kg ºC) at 350ºC and let the stone and water come to an equilibrium temperature with no heat loss, what temperature would it be?
5. How much energy does it take to heat 5kg of ice at -50ºC to 150ºC? The latent heat of fusion for ice is Lf = 334 kJ/kg and the latent heat of vaporization is Lv = 2257 kJ/kg.
6. How much -10ºC ice must you add to 10L of 0ºC water to freeze all the water? Latent head of fusion for ice is Lf = 334 kJ/kg.
7. You drop a penny, mass = 2.5g, in a vacuum tube so there is no air resistance and the penny hits the ground and becomes liquid from the impact.  If the penny started at 25ºC  and the heat capacity, latent heat of fusion and melting point of copper are; cv = 385 J/kg ºC, Lf = 207 kJ/kg and 1085ºC, what is the minimum height you could have dropped the penny from?
8. Let’s say you wanted to heat a bath by firing a machine gun into the water.  If each bullet has a mass of 50g and a velocity of 280m/s how many bullets would you have to fire into an 80L tub of water to raise its temperature 10ºC? Assume all the bullet’s mechanical energy goes to heating the water and neglect the mass of bullets in the tub.

#### Entropy

1. What is the change in entropy when 10kg of ice is melted into water at  0ºC? How about when 10kg of water is turned into steam at 100ºC?
2. What is the change in entropy when 5kg of dry ice is vaporized at -56.6ºC if the latent heat of vaporization for carbon dioxide is 574 kJ/kg?