Solved Problem on Heat

A body has a mass of 500 grams and specific heat of 0.4 g/cal°C. Determine:
a) The quantity of heat that the body should receive to ensure that its temperature varies from 5 °C to 35 °C;
b) The quantity of heat that the body must give so its temperature decreases from 15 °C.

Problem data:

Mass of body: m = 500 g;
Specific heat: c = 0.4 g/cal°C.

Solution

a) The initial temperature t_i = 5 °C and the final temperature t_f = 35 °C the quantity of heat that the body should receive to occur heating will be given by the equation heat

\[ \begin{gather} \bbox[#99CCFF,10px] {Q=mc\Delta t} \tag{I} \end{gather} \]

\[ \begin{gather} Q=mc(t_{f}-t_{i})\\ Q=500\times 0.4\times (35-5)\\ Q=200\times 30 \end{gather} \]

\[ \bbox[#FFCCCC,10px] {Q=6000\;\text{cal}} \]

b) If the heat is lost Δt<0, therefore the variation should be Δt = −15 °C, and the lost heat will be given using the expression (I)

\[ \begin{gather} Q=mc\Delta t\\ Q=500\times 0.4\times (-15) \end{gather} \]

\[ \bbox[#FFCCCC,10px] {Q=-3000\;\text{cal}} \]

Note: In item (a), the temperature varies from an initial value t_i to a final value t_f, we know the initial and final values of the temperature. In item (b), the temperature varies from a certain value, we know the variation Δt without knowing the values initial and final ?of the temperature.

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