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?

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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" #