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

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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STEP 1   State the given and needed quantities.

ANALYZE THE PROBLEM Given Need Connect
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 Heat ofvaporizationjoules Metricfactorkilojoules  \boxed{\begin{array}{l}\text{Heat of}\\vaporization \end{array}}\rightarrow \text{joules}  \boxed{\begin{array}{l}\text{Metric}\\factor\end{array}}\rightarrow \text{kilojoules} 

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

1 g of H2O(lg)=2260 J2260 J 1 g of H2O and 1 g of H2O2260 J 1 kJ = l000 J l000 J 1 kJ  and 1 kJl000 J \begin{array}{r c}\boxed{\begin{matrix} 1  g  of  H_{2}O(l \rightarrow g) = 2260  J \\\frac{\text{2260 J }}{1  g  of  H_{2}O } \text{ and } \frac{1  g  of  H_{2}O }{\text{2260 J }} \end{matrix}} & \boxed{\begin{matrix} \text{1 kJ = l000 J }\\ \frac{\text{l000 J }}{\text{1 kJ }}\text{ and }\frac{\text{1 kJ}}{\text{l000 J }} \end{matrix}}\end{array}

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

Heat=122 g H2OThree SFs× 2260 J1 g H2O ExactThreeSFs×1 KJ1000 JExactExact=276 KJThree SFs \boxed{Heat} = \underset{Three  SFs }{\boxed{122  \cancel{g  H_{2}O}}} \times  \overset{Three SFs}{\underset{Exact }{\boxed{\frac{2260  \cancel{J}}{1  \cancel{g  H_{2}O}  } }}} \times \overset{Exact}{\underset{Exact }{\boxed{\frac{1  KJ}{1000  \cancel{J}} }}} = \underset{Three  SFs}{276  KJ}

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STEP 1   State the given and needed quantities. ...