Question

A 115-g sample of steam at ${100}^{o}C$is emitted from a volcano. It condenses, cools, and falls as snow at $0^{o}C$. How many kilojoules were released?

Short answer

$346kJ$were released

Step-by-step solution

Step 1:  Introduction

Mass of steam released is $115g$and specific heat of water $c=1.0\mathrm{cal}/{\mathrm{g}}^0\mathrm{C}$

After condensation of steam heat released is localid="1654282579212" $540\mathrm{cal}/\mathrm{g}$

The heat of fusion of water after condensing is localid="1654282583440" $79.7\mathrm{cal}/\mathrm{g}$

The heat released after condensation of steam =localid="1654282587786" $\frac{115\times 540}{1000}=62kcal$

The heat released after condensation of water =localid="1654282592134" $\frac{115\times 79.9}{1000}=9.17kcal$

Explanation 

Temperate change $∆T={100}^{o}C-0^{o}C={100}^{o}C$

Heat released $Q=mc\mathrm{\Delta }T$

localid="1654282600172" $\Rightarrow \frac{115\times 79.7}{1000}=9.17kcal$

The total heat released from the steam is

localid="1654282618969" $$\begin{gathered} =62\mathrm{kcal}+11.5\mathrm{kcal}+9.17\mathrm{kcal} \\ =82.17\mathrm{kcal} \\ =82.17\times 4.184(1kcal=4.184J) \\ =346kJ \end{gathered}$$