Some very hot rocks have a temperature of #170 ^o C# and a specific heat of #300 J/(Kg*K)#. The rocks are bathed in #56 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 · 2018-01-08T16:15:09

The mass of the rocks is #=6018.7kg#

The heat transferred from the hot rocks to the water, is equal to the heat used to evaporate the water.

For the rocks #DeltaT_o=170-100=70^@#

Heat of vaporisation of water is

#H_w=2257kJkg^-1#

The specific heat of the rocks is

#C_o=0.3kJkg^-1K^-1#

The mass of water is #m_w=56kg#

# m_o C_o (DeltaT_o) = m_w H_w #

#m_o*0.3*70=56*2257#

The mass of the rocks is

#m_o=(56*2257)/(0.3*70)#

#=6018.7kg#