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A chemist carefully measures the amount of heat needed to raise the temperature of a 1.28kg sample of a pure substance from 11.1°C to 17.0°C. The experiment shows that 14.kJ of heat are needed. What can the chemist report for the specific heat capacity of the substance? Round your answer to 2 significant digits.

Question

A chemist carefully measures the amount of heat needed to raise the temperature of a 1.28kg sample of a pure substance from 11.1°C to 17.0°C. The experiment shows that 14.kJ of heat are needed. What can the chemist report for the specific heat capacity of the substance? Round your answer to 2 significant digits.

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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 kilograms or kg) c = specific heat capacity (in joules per kilogram per degree Celsius or J/kg°C) ΔT = change in temperature (in degrees Celsius or °C)

In this case, we are given: q = 14 kJ = 14,000 J (since 1 kJ = 1,000 J) m = 1.28 kg ΔT = 17.0°C - 11.1°C = 5.9°C

We are asked to find c. Rearranging the formula to solve for c gives us:

c = q / (mΔT)

Substituting the given values into this formula gives us:

c = 14,000 J / (1.28 kg * 5.9°C) = 1,900 J/kg°C

Rounding to two significant figures gives us a specific heat capacity of 1.9 kJ/kg°C.

This problem has been solved

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