Question

a chemist carefully measures the amount of heat needed to raise the temperature of a 835.0 mg sample of a pure substance from -0.8 °c to 11.5 °c. the experiment shows that 7.29 j of heat are needed. what can the chemist report for the specific heat capacity of the substance? be sure your answer has the correct number of significant digits.

Explanation:

Step1: Convert mass to kg

$835.0\ mg=835.0\times10^{- 6}\ kg = 8.350\times10^{-4}\ kg$

Step2: Calculate the change in temperature

$\Delta T=T_2 - T_1=(11.5+273.15)-(-0.8 + 273.15)=12.3\ K$

Step3: Use the specific - heat formula $c=\frac{q}{m\Delta T}$

$c=\frac{7.29\ J}{8.350\times10^{-4}\ kg\times12.3\ K}\approx710\ J\cdot kg^{-1}\cdot K^{-1}$

Step4: Determine significant digits

The mass has 4 significant digits, the heat has 3 significant digits, and the temperature change has 3 significant digits. So the result should have 3 significant digits. Rounding $710\ J\cdot kg^{-1}\cdot K^{-1}$ to 3 significant digits gives $710\ J\cdot kg^{-1}\cdot K^{-1}$

Answer:

$710\ J\cdot kg^{-1}\cdot K^{-1}$