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Our observations have already shown us that the temperature change is double for half as much water. We can repeat these observations for many different masses of water, and we also find that the temperature change is inversely proportional to the mass of the water. This means that the heat capacity C itself is proportional to the mass of the substance heated. (Look back at Equation 1 to convince yourself that this is true. For a fixed amount of heat, what happens to the temperature change and the heat capacity if we double the mass of water heated?) So now we rewrite Equation 1 with this new information:

q = m C s ΔT

Here, m is the mass of the material being heated, and the proportional constant is now called the “heat capacity per gram” or more commonly the “specific heat.” Experiments show that, for any particular material, C s is a relatively constant property of the material. (C s actually varies slowly with the temperature, so it is about constant unless we make very large temperature changes.)

This equation so far is not very helpful, though, because we do not know values for the heat q or for the specific heat C s . If we knew one, we would know the other from Equation 2, so somehow we have to devise an experiment to measure one or the other.

Here’s one way to do the experiment. Since heat is a form of energy and energy is the capacity to do work, we just need to measure how much work can be done for a specific amount of heat, e.g. for burning a specific amount of methane. This is tricky, but we’ve already seen that we can use the heat generated by a reaction to push a piston back in a cylinder. If we burn 1.0 g of methane, we can measure how much work is done on the piston by measuring how much force is generated and for what distance. From these measurements and the rules of physics, we find that burning 1.0 g of methane can produce a maximum amount of work equal to 55.65 kJ.

(A second way to do the experiment is to use work to increase the temperature of water and to measure how much work is required to increase the temperature of water by 1 °C. We’ll leave it as an exercise to devise a way to elevate temperature by doing work.)

What do the data tell us? If 55.65 kJ of work can be done by burning 1.0 g of methane, then burning 1.0 g of methane must produce 55.65 kJ of heat. This is q in Equation 2. But we have already measured that, for 1.0 kg of water, the temperature change is 13.3°C. This is ΔT in Equation 2, and m is 1000 g. From these data, we can directly calculate that, for water, C s = 4.184 J/g·°C. This is called the specific heat of water, or somewhat more loosely, the heat capacity of water. Pay attention to the units of this quantity, as they are unusual.

In similar ways, it is possible to find the specific heat or heat capacity of any material of interest. A set of specific heats for different substances is shown in [link] . This is very valuable for predicting temperature changes in different materials. For our purposes, it has an even greater value. We can use this to determine the energy change in a chemical reaction.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Concept development studies in chemistry 2013. OpenStax CNX. Oct 07, 2013 Download for free at http://legacy.cnx.org/content/col11579/1.1
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