In a sauna, 122 g of water is converted to steam at 100 °C. How many kilojoules of heat are needed?

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Accepted Answer

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM	Given	Need	Connect
ANALYZE THE PROBLEM	122 g of water at 1oo °C	kilojoules to convert to steam at 100 °C	heat of vaporization, 2260 J/g

STEP 2 Write a plan to convert the given quantity to the needed quantity.

grams of water [latex] \boxed{\begin{array}{l} ext{Heat of}\vaporization \end{array}} ightarrow ext{joules} \boxed{\begin{array}{l} ext{Metric}\factor\end{array}} ightarrow ext{kilojoules} [/latex]

STEP 3 Write the heat conversion factor and any metric factor.

[latex]\begin{array}{r c}\boxed{\begin{matrix} 1 g of H_{2}O(l ightarrow g) = 2260 J \\frac{ ext{2260 J }}{1 g of H_{2}O } ext{ and } \frac{1 g of H_{2}O }{ ext{2260 J }} \end{matrix}} & \boxed{\begin{matrix} ext{1 kJ = l000 J }\ \frac{ ext{l000 J }}{ ext{1 kJ }} ext{ and }\frac{ ext{1 kJ}}{ ext{l000 J }} \end{matrix}}\end{array} [/latex]

STEP 4 Set up the problem and calculate the needed quantity.

[latex] \boxed{Heat} = \underset{Three SFs }{\boxed{122 \cancel{g H_{2}O}}} imes \overset{Three SFs}{\underset{Exact }{\boxed{\frac{2260 \cancel{J}}{1 \cancel{g H_{2}O} } }}} imes \overset{Exact}{\underset{Exact }{\boxed{\frac{1 KJ}{1000 \cancel{J}} }}} = \underset{Three SFs}{276 KJ} [/latex]

Question 3.8: In a sauna, 122 g of water is converted to steam at 100 °C. ...

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