Question

Some very hot rocks have a temperature of `220 ^o C` and a specific heat of `250 J/(Kg*K)`. The rocks are bathed in `40 L` of boiling water. If the heat of the rocks completely vaporizes the water, what is the minimum combined mass of the rocks?

Answer 1

The mass of the rocks is `=30009.3kg`

Explanation:

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=220-100=120^@`

Heat of vaporisation of water is

`H_w=2257kJkg^-1`

The specific heat of the rocks is

`C_o=0.25kJkg^-1K^-1`

Volume of water is `V=40L`

Density of water is `rho=1kgL^-1`

The mass of water is `m_w=Vrho=40kg`,

`m_o C_o (DeltaT_o) = m_w H_w`

`m_o*0.25*120=40*2257`

The mass of the rocks is

`m_o=(40*2257)/(0.25*120)`

`=3009.3kg`