Question:
How would the energy needed to change 10 grams of water by 1 degree Celsius, be compared to changing 100 grams of water by 1 degree Celsius? This question has got to do with specific heat capacity. Thank you
Response by Eric Chisholm:
This question is from the area of thermodynamics:
First off the specific heat capacity (or more commonly specific heat) of a material is a measure of the amount of ‘heat’ required to raise the temperature, of a sample, by a unit of temperature. Since you are increasing your sample size by ten times (i.e. 10 to 100) intuition should tell you that the heat required will increase and as expected this is the case! To keep things as simple as possible let us assume that both samples are initially at 20 degrees and both at the same pressure. We are doing this to limit the differences between the two set-ups and minimize the complexity of the problem. This way the answer and analysis can focus on what you describe as the significant change in your experiment, namely, the change in mass. Under these circumstances we can use the following formula:
Q (heat required) = m (mass) * dT (difference or change in temperature) * c (specific heat constant)
The specific heat constant denoted as ‘c’ has units of: J/(g*K). The ‘J’ represents units of energy known as Joules, ‘g’ represents mass in grams and ‘K’ represents our temperature scale in kelvins. Since your question uses Celsius it should be noted that a change of 1 K is equal to a change of 1 degree Celsius.
In this case, for both samples the temperature change and the specific heat constant are the same so after simplifying all we are left with is the change in mass. Since our sample increases by a factor of 10 the amount of ‘heat’ required will also increase by a factor of 10. Mathematically we can produce this ratio as follows:
Q(sample 2 )/ Q(sample 1) =
[m(sample2) * dT(sample2) * c] / [m(sample1) * dT(sample1) * c]
Since dT(sample2) and dT(sample1) are equal (i.e. 1 in this case) they, along with the ‘c’ term which is common to both top and bottom, cancel and you are left with:
Q2 / Q1 = m2 / m1 = 100/10 = 10
* If we were to change the experiment so that the samples were subjected to different conditions (examples of these changes could include holding the samples at different pressures or selecting a change in the temperature that would cause one of the samples to undergo a phase change) our end answer would change. *
Heat Recovery and Burner Technologies
Participants at the Advanced Integrated Energy Efficiency Solutions Energy 2011 workshop benefited from presentations on the latest technologies under development for waste heat recovery and furnace optimization. Representatives from CanmetENERGY (Ottawa and Varennes Research Centres) and Cameron Veitch of ConDex Systems, discussed the potential energy savings that can be gained from implementation of advanced technologies.
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Heat Recovery and Burner Technologies