Solved Problem on Heat

Bandeira do Brasil  Portugu√™s    Flag of the United Kingdom  English
A body made of 250 g of brass is heated from 0°C to 100°C, it is used 2300 cal to heat the body. Find:
a) The specific heat of the brass;
b) The heat capacity of the body;
c) If the body in the final situation loses 1000 cal, what will be its temperature?

Problem data Solution

a) Using the relationship between heat and temperature change we can find the specific heat
\[ \bbox[#99CCFF,10px] {Q=mc\Delta t} \]
\[ c=\frac{Q}{m(\;t_{\text{f}}-t_{\text{i}}\;)}\\ c=\frac{2300}{250(\;100-0\;)}\\ c=\frac{23 \cancel{{00}}}{250 \cancel{{00}}}\\ c=\frac{23}{250} \]
\[ \bbox[#FFCCCC,10px] {c=0.092\;\text{cal/g}^{\text{o}}\text{C}} \]

b) The heat capacity of the body
\[ \bbox[#99CCFF,10px] {C=mc} \]
\[ C=250 \times 0.092 \]
\[ \bbox[#FFCCCC,10px] {C=23\;\text{cal/}^{\text{o}}\text{C}} \]

c) If the body loses heat we have Q = −1 000 cal, the temperature of 100°C becomes the initial temperature of the body and we want the final temperature
\[ \bbox[#99CCFF,10px] {Q=mc\Delta t} \]
\[ -1000=250 \times 0.092 \times (\;t_{\text{f}}-100\;)\\ -1000=23 \times (\;t_{\text{f}}-100\;)\\ t_{\text{f}}-100=\frac{-{1000}}{23}\\ t_{\text{f}}=-43.5+100 \]
\[ \bbox[#FFCCCC,10px] {t_{\text{f}}=56.5\;^{\text{o}}\text{C}} \]