Specific and latent heat

Problem:

If 90 g of molten lead at 327.3 oC is poured into a 300 g casting form made of iron and initially at 20 oC, what is the final temperature of the system?  Assume no energy is lost to the environment.

Solution:

Problem:

Pure water can be super-cooled at standard atmospheric pressure to below its normal freezing point of 0 °C.  Assume that a mass of water has been cooled as a liquid to –5 °C, and a small (negligible mass) crystal of ice is introduced to act as a “seed” or starting point of crystallization.  If the subsequent change of state occurs adiabatically and at constant pressure, what fraction of the system solidifies?  Assume the latent heat of fusion of the water is 80 kcal/kg and that the specific heat of water is 1 kcal/(kg oC).

Solution:

Problem:

A liquid of unknown specific heat at a temperature of 20°C was mixed with water at 80°C in a well-insulated container.  The final temperature was measured to be 50°C, and the combined mass of the two liquids was measured to be 240-g.  In a second experiment with both liquids at the same initial temperatures, 20-g less of the liquid of unknown specific heat was poured into the same amount of water as before.  This time the equilibrium temperature was found to be 52°C.  Determine the specific heat of the liquid.  The specific heat of water is 4187 J/Kg°C or 1 kcal/kg°C.

Solution:

Problem:

An electric coffee pot contains 2 liters of water which it heats from 20o C to boiling in 5 minutes.  The supply voltage is 120V and each kWh costs 10 cents.  Calculate
(a) the electric power converted,
(b) the cost of making ten pots of coffee,
(c) the resistance of the heating element, and
(d) the current in the element.

Solution:

Problem:

How much thermal energy is required to change a 40 g ice cube from a solid at -10 oC to steam at 110 oC?

Solution:

Problem:

A capacitor, C = 100 μF, is charged to a potential of 25 kV.  The capacitor is then discharged through a 1 kW resistor immersed in and at equilibrium with 500 ml of water.  The water is at an initial temperature of 20 oC.  Find the final, equilibrium temperature of the water (specific heat 4187 J/kgoC), if the resistor has specific heat of 710 J/kgoC and a mass of 100 g.

Solution:

Problem:

In his short story "A Slight Case of Sunstroke", Arthur C. Clarke writes of a stadium full of disgruntled soccer fans barbecuing the dishonest referee by reflecting sunlight on him with mirrors found under their seats.
(a)  Imagine a stadium at the equator at noon (i.e. the sun's directly overhead), with 50,000 fans. Assuming that sunlight delivers about 1000 watts per square meter to the surface of the Earth, and that each fan is holding a 0.25 m2 mirror at 45o, how much power would be available to be projected onto a dishonest referee?
(b)  To be humane, let us replace the referee with a 50 kg cylinder of 37 oC water.  Assuming this cylinder absorbs all of the reflected light from the mirror - wielding fans, how long will it take for it to reach 100 oC?  (The heat capacity of water is about 4200 J/(kgoC).)

Solution:

Problem:

In a solar collector, water flows through pipes that collect heat from an area of 10 m2.  The collector faces the Sun and the intensity of sunlight incident on it is 2000 W/m2.  At what rate (in kg/minute) should the water circulate through the pipes so that it is heated by 40oC, if the collector efficiency is 30%?  (The specific heat of water is c = 4200 J/(kg oC)).

Solution:

Problem:

Phonons are quantized lattice vibrations, and many aspects of these excitations can be understood in terms of simple mode counting.
(a)  Estimate the number of phonon modes in 1 cm3 of a crystalline material with an inter-atomic spacing of 2 Angstrom.
(b)  Assuming that in thermal equilibrium each phonon mode has kBT of energy, give a numerical estimate of the heat capacity ΔE/ΔT of this 1 cm3 of material, in [J/K].

Problem:

Let CP and CV denote the molar specific heat of an ideal gas at constant pressure and at constant volume, respectively.  Show that CP - CV = R.

Solution:

Problem:

Let CP and CV denote the molar specific heat of an ideal diatomic gas at room temperature at constant pressure and constant volume, respectively.  Find the ratio CP/CV.

Solution: