# Calculate the amount of heat (in kJ) required to raise the temperature of 186 grams of water from 29◦C to 69◦C. (The specific heat of water is 4.18 J/g· ◦C.)

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Expert Answers

t-nez | Certified Educator

Specific heat is the amount of heat required to raise the temperature of one gram of a substance one degree celsius. The equation for calculating the amount of heat required for a given temperature change in a given mass of substance is:

q = mc `Delta` T where:

q = heat

m = mass = 186g

c = specific heat = 4.186 Joules/gram-ºC

`Delta` T = change in temperaturge = 69ºC-29ºC = 4ºC

q = (186 g)(4.186 J/g-ºC)(40ºC) = 31,099 J = 31,000 J rounded to 2 significant digits.

To change this value to kilojoules, multiply by the conversion factor 1kJ/1000 J:

(31,000 J)(1 kJ/1000 J) = **31 kJ**

Another method of calculating the answer is kJ is to change the specific heat of water to kJ/g-ºC:

(4.186 J/g-ºC)(1 kJ/1000 J) = .004186 kJ/g-ºC