1.4 Heat transfer, specific heat, and calorimetry  (Page 4/14)

Calculating the required heat

A 0.500-kg aluminum pan on a stove and 0.250 L of water in it are heated from $20.0\text{°}\text{C}$ to $80.0\text{°}\text{C}$ . (a) How much heat is required? What percentage of the heat is used to raise the temperature of (b) the pan and (c) the water?

Strategy

We can assume that the pan and the water are always at the same temperature. When you put the pan on the stove, the temperature of the water and that of the pan are increased by the same amount. We use the equation for the heat transfer for the given temperature change and mass of water and aluminum. The specific heat values for water and aluminum are given in [link] .

Solution

1. Calculate the temperature difference:
   
   $\text{Δ}T=T_{\text{f}}-T_{\text{i}}=60.0\text{°}\text{C}.$
2. Calculate the mass of water. Because the density of water is $1000{\text{kg/m}}^3$ , 1 L of water has a mass of 1 kg, and the mass of 0.250 L of water is $m_w=0.250\text{kg}$ .
3. Calculate the heat transferred to the water. Use the specific heat of water in [link] :
   
   $Q_{\text{w}}=m_{\text{w}}{c}_{\text{w}}\text{Δ}T=\left(0.250\text{kg}\right)\left(4186\text{J/kg}\text{°}\text{C}\right)\left(60.0\text{°}\text{C}\right)=62.8\text{kJ}.$
4. Calculate the heat transferred to the aluminum. Use the specific heat for aluminum in [link] :
   
   $Q_{\text{Al}}=m_{\text{A1}}{c}_{\text{A1}}\text{Δ}T=\left(0.500\text{kg}\right)\left(\text{900}\text{J/kg}\text{°}\text{C}\right)\left(60.0\text{°}\text{C}\right)=27.0\text{kJ}.$
5. Find the total transferred heat:
   
   $Q_{\text{Total}}=Q_{\text{W}}+Q_{\text{Al}}=89.8\text{kJ}.$

Significance

In this example, the heat transferred to the container is a significant fraction of the total transferred heat. Although the mass of the pan is twice that of the water, the specific heat of water is over four times that of aluminum. Therefore, it takes a bit more than twice as much heat to achieve the given temperature change for the water as for the aluminum pan.

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