Some very hot rocks have a temperature of #360 ^o C# and a specific heat of #840 J/(Kg*K)#. The rocks are bathed in #16 L# of water at #40 ^oC#. 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 · 2017-04-20T10:09:51

The mass of the rocks is #=183.7kg#

The heat transferred from the rocks to the water, is equal to the heat used to heat the water to 100ºC and evaporate it.

For the rocks #DeltaT_o=360-100=260º#

For the water #DeltaT_w=100-40=60º#

# m_o C_o (DeltaT_o) = m_w H_w +m_w*C_w*DeltaT_w#

Heat of vaporisation of water

#H_w=2257kJkg^-1#

#C_w=4.186kJkg^-1K^-1#

#C_o=0.84kJkg^-1K^-1#

#m_o*260*0.84=16*(2257+4.186*80)#

#m_o=(16*(2257+4.186*60))/(260*0.84)#

#=183.7kg#