Question

Answer the following questions involving specific heat capacities :

a ) How much energy is required to change 42 g ice cube from ice at -11°C to steam at 111°C?

b ) 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?

c ) 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

Part -a

GIven is :-

mass of the ice cube m=42 g or 0.042 Kg

Initial temperature = -11 C Final temperature = 111 C

Specefic heat for water for different phases is :-

c for ice 2.108 kJ/kg-K
c for water 4.187 kj/kg-K
c for steam 1.996 kJ/-kgK

Similarly latent heat is:-

L for ice to water = 337kJ/kg
L for water to steam 2258kJ/kg

This process involves three main steps.

E = (heat energy required for ice to go from -11ºC to 0ºC) + (latent heat energy for ice at 0ºC to convert to water at 0ºC) + (heat energy for water to go from 0ºC to 100ºC) + (latent heat energy for water at 100ºC to convert to steam at 100ºC) + (heat energy for steam at 100ºC to steam at 111ºC)

Formula for heat energy required to change in temperature while in same state will be given by:-

and formula for latent heat energy is

Thus by putting all the values for all the phases and adding them up will given us our desired result.

THus

E = 0.042*2.108*11 + 0.042*337 + 0.042*4.187*100 + 0.042*2258 + 0.042*1.996*11
E = 128.471448kJ = 128471.448J