Some very hot rocks have a temperature of #960 ^o C# and a specific heat of #250 J/(Kg*K)#. The rocks are bathed in #50 L# of boiling water. If the heat of the rocks completely vaporizes the water, what is the minimum combined mass of the rocks?

Question

1400 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-02T01:02:17

The minimum combined mass of the rocks is #518.6# Kg.

The latent heat of vaporization of water is #2230 " kJ/Kg"#. The net amount of heat needed to vaporize #50 " l"#, i,e, #50" Kg"# of boiling water is

#2230 times 50 " kJ" = 1.115times 10^7 " J"#

Now, the least temperature that the hot rocks can reach is #100^circ"C"#. So, the maximum heat available from them is

#250 times (960-100) times M " J/Kg" = 2.15times10^5M" J/Kg" #,

if their combined mass is #M#. Thus,

#2.15times 10^5 M" J/Kg" ge 1.115times 10^7 " J"#

or hence

#M ge 518.6 " Kg" #