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?

Question

1955 views around the world

You can reuse this answer
Creative Commons License

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#