Question

An igloo is made of 137 blocks of ice at 0°C, each with a mass of 3 kg. How much heat must be gained by the ice in order to melt the entire igloo?

Answer 1

`\begin{equation*} 9.29*10^8J \end{equation*}`

Step-by-step explanation

First, let us find the total mass of the blocks of ice:

`\begin{gathered} m=137*3 \\ m=411\text{ }kg \end{gathered}`

To find the amount of heat that must be gained, apply the formula for the heat change due to vaporization:

`\Delta Q=mh_v`

where hv = heat of vaporization = 2.26 * 10⁶ J/kg

Therefore, the amount of heat that must be gained is:

`\begin{gathered} \Delta Q=411*2.26*10^6 \\ \Delta Q=928.86*10^6J \\ \Delta Q=9.29*10^8J \end{gathered}`

That is the answer.