Question

a) Liquid nitrogen, which has a boiling point of 77 K, is commonly used to cool substances to low temperatures. How much energy must be removed from 1.0 kg of gaseous nitrogen at 77 K for it to completely liquefy?

b) How much energy is needed to melt 0.225 kg of lead so that it can be used to make a lead sinker for fishing? The sample has an initial temperature of 27.3°C and is poured in the mold immediately after it has melted.

Answer 1

A)

To solve this, you need to know the latent heat of vaporization (enthlalpy of vaporization) of N2which is around 5.57 kJ/mol. N2 has a molecular mass of 28 gm/mol, so in terms of mass, the enthalpy of vaporization is (5.57 kJ/mol)/(28 gm/mol) = 198.93 J/gm = 198.93 kJ/kg.

The enthalpy of vaporization tells you how much energy is liberated when a unit amount (mole or kg) of liquid N2 is converted to gaseous N2, or, conversely, how much energy must be removed to convert the gas to a liquid.

To convert 1 kg of gaseous nitrogen at 77K (the boiling point of N2 at 1 atm pressure) to liquid nitrogen,

1kg * 198.93 kJ/kg = 198.93 kJ = 1.99*10^5 J (which rounds to 2.0*10^5 J)

of energy must be removed.

B)

Lead Specific Heat = 0.130 j/g/°C

Latent Heat = 22.4kJ/kg

Melting Point = 328°C

The lead is first heated from 27.3 to 328°C = ΔT = 300.7°

...Sensible heat = 300.7 x 0.13 x 0.225 = 8.796 kJ

The Lead is then melted:

*..Latent heat = 0.225 x 22.4 = 5.04 kJ

*...Total heat energy required = 8.795 + 5.04 = 13.835 kJ