Problems on Heat and Thermodynamics

1. A cube 10 cm on each edge contains air (equivalent molar mass 28.9 g/mol) at atmospheric pressure and temperature 27 degree C. Find the mass of gas, its weight, and the force it exerts on each face of the cube. Comment on the physical reason why such a small sample can exert such a great force.

2. In a time t, N hailstones strike a glass window of area A at angle theta to the window surface. Each hailstone has a mass m and a speed v. If the collisions are elastic, what are the average force and the pressure on the window?

3. Use the definition of Avogadro's number to find the mass of a helium atom.

4. A 5 L vessel contains nitrogen gas at 27 degree C and 3 atm. Find the total kinetic energy of the gas molecules and the average kinetic energy per molecule.

5. Suppose you breathe out 22 breaths per minute, each with volume of 0.6 L. Assume you inhale dry air and exhale air at 37 degree C containing water vapor with a vapor pressure of 3.2 kPa. The vapor comes from evaporation of liquid water in your body. Model the water vapor as an ideal gas. Assume its latent heat of evaporation at 37 degree C is the same as its heat of evaporation at 100 degree C (Lembda = 2.26*10^6 J/kg). Calculate the rate of your energy loss by exhaling humid air.

6. An ideal gas is enclosed in a cylinder that has a movable piston on top. The piston has a mass m and an area A, and is free to slide up and down keeping the pressure of the gas constant. How much work is done on the gas as the temperature of n mol of gas is raised from T1 to T2?

7. 5 mol of air at 20 degree C and 1 atm are compressed to one tenth of the original volume by (a) an adiabatic process (PV^gamma =const, where gamma = Cp/Cv) and (b) an isothermal process (PV = const). What is the final pressure and temperature in each of these cases?

8. A Carnot engine has a useful power output of 150 kW. The engine operates between two reservoirs at 20 degree C and 500 degree C. How much energy does it absorb per hour? How much energy is expelled per hour in its exhaust?

9. If mass mh of water at Th is poured into an aluminum cup of mass mAl containing mass mc of water at Tc, where Th>Tc, what is the equilibrium temperature of the system? [Th = T subscript h, mAl = m subscript Al etc.]