A chemist carefully measures the amount of heat needed to raise the temperature of a 832.0g sample of a pure substance from 26.3°C to 37.4°C. The experiment shows that 17.1kJ of heat are needed. What can the chemist report for the specific heat capacity of the substance? Round your answer to 3 significant digits.
Question
A chemist carefully measures the amount of heat needed to raise the temperature of a 832.0g sample of a pure substance from 26.3°C to 37.4°C. The experiment shows that 17.1kJ of heat are needed. What can the chemist report for the specific heat capacity of the substance? Round your answer to 3 significant digits.
Solution
The specific heat capacity (c) of a substance can be calculated using the formula:
q = mcΔT
where: q = heat energy absorbed or released (in joules or J) m = mass of the substance (in grams or g) c = specific heat capacity (in J/g°C) ΔT = change in temperature (in °C)
In this case, we are given: q = 17.1 kJ = 17100 J (since 1 kJ = 1000 J) m = 832.0 g ΔT = 37.4°C - 26.3°C = 11.1°C
We are asked to find c. Rearranging the formula to solve for c gives:
c = q / (mΔT)
Substituting the given values into the formula gives:
c = 17100 J / (832.0 g * 11.1°C) = 1.85 J/g°C
So, the specific heat capacity of the substance is 1.85 J/g°C, rounded to three significant digits.
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