Solve problems involving heat transfer to and from ideal monatomic gases whose volumes are held constant
Solve similar problems for non-monatomic ideal gases based on the number of degrees of freedom of a molecule
Estimate the heat capacities of metals using a model based on degrees of freedom
In the chapter on temperature and heat, we defined the specific heat capacity with the equation
$Q=mc\text{\Delta}T,$ or
$c=(1\text{/}m)Q\text{/}\text{\Delta}T$ . However, the properties of an ideal gas depend directly on the number of moles in a sample, so here we define specific heat capacity in terms of the number of moles, not the mass. Furthermore, when talking about solids and liquids, we ignored any changes in volume and pressure with changes in temperature—a good approximation for solids and liquids, but for gases, we have to make some condition on volume or pressure changes. Here, we focus on the heat capacity with the volume held constant. We can calculate it for an ideal gas.
Heat capacity of an ideal monatomic gas at constant volume
We define the
molar heat capacity at constant volume${C}_{V}$ as
If the volume does not change, there is no overall displacement, so no work is done, and the only change in internal energy is due to the heat flow
$\text{\Delta}{E}_{\text{int}}=Q.$ (This statement is discussed further in the next chapter.) We use the equation
${E}_{\text{int}}=3nRT\text{/}2$ to write
$\text{\Delta}{E}_{\text{int}}=3nR\text{\Delta}T\text{/}2$ and substitute
$\text{\Delta}E$ for
Q to find
$Q=3nR\text{\Delta}T\text{/}2$ , which gives the following simple result for an ideal monatomic gas:
${C}_{V}=\frac{3}{2}R.$
It is independent of temperature, which justifies our use of finite differences instead of a derivative. This formula agrees well with experimental results.
In the next chapter we discuss the molar specific heat at constant pressure
${C}_{p},$ which is always greater than
${C}_{V}.$
Calculating temperature
A sample of 0.125 kg of xenon is contained in a rigid metal cylinder, big enough that the xenon can be modeled as an ideal gas, at a temperature of
$20.0\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$ . The cylinder is moved outside on a hot summer day. As the xenon comes into equilibrium by reaching the temperature of its surroundings, 180 J of heat are conducted to it through the cylinder walls. What is the equilibrium temperature? Ignore the expansion of the metal cylinder.
Solution
Identify the knowns: We know the initial temperature
${T}_{1}$ is
$20.0\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$ , the heat
Q is 180 J, and the mass
m of the xenon is 0.125 kg.
Identify the unknown. We need the final temperature, so we’ll need
$\text{\Delta}T$ .
Determine which equations are needed. Because xenon gas is monatomic, we can use
$Q=3nR\text{\Delta}T\text{/}2.$ Then we need the number of moles,
$n=m\text{/}M.$
Substitute the known values into the equations and solve for the unknowns.
The molar mass of xenon is 131.3 g, so we obtain
Therefore, the final temperature is
$35.2\phantom{\rule{0.2em}{0ex}}\text{\xb0C}$ . The problem could equally well be solved in kelvin; as a kelvin is the same size as a degree Celsius of temperature change, you would get
$\text{\Delta}T=15.2\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$
Significance
The heating of an ideal or almost ideal gas at constant volume is important in car engines and many other practical systems.
I'm not sure about it, but I think it's possible.
If you add some form of energy to the system, it's a possibility.
Also, if you change the pression or the volume of the system, you'll increase the kinetic energy of the system, increasing the gas temperature.
I don't know if I'm correct.
playdoh
For example, if you get a syringe and close the tip(sealing the air inside), and start pumping the plunger, you'll notice that it starts getting hot.
Again, I'm not sure if I am correct.
playdoh
you are right for example an adiabatic process changes all variables without external energy to yield a temperature change. (Search Otto cycle)
it is a theory in which time is taken as relative,for diff. motion of objects.
Antares
no !!!
jyotirmayee
it is E=mc'square
jyotirmayee
what is black hole?
jyotirmayee
E=mc^2 is just a reln which sums up everything dude
Antares
what does e=mc^2 stand for?explain
Piyali
m not dude
jyotirmayee
e for speed of light
jyotirmayee
c for speed of light
jyotirmayee
m for mass of object
jyotirmayee
black hole is a super massive object in space gravitation pull of which s so strong dt evn light cannot escape. John wheeler 1st detected it, n concept of it ws given by Einstein himself from his general theory of relativity. Basically v cn si 3 types of it super massive, interstellar n intermediate
Antares
which topic now u studying?
jyotirmayee
e defined? sorry it,s wrong
jyotirmayee
how black holes r formed?
Piyali
e is not speed of light
jyotirmayee
black holes formed when the centre of very massive star collapsed itself
jyotirmayee
e is energy.
Antares
what do u mean by quantum mechanics?
jyotirmayee
in most of d cases black holes r formed by massive collapsed star or star system
Antares
sahoo u don't seem to understand relative physics, plz study that first.
Antares
Apollo is the name of a satellite !!!!!
jyotirmayee
quantum mechanics is d study of physics describing nature at d smallest level of energy of atoms n subatomic particles.
Antares
qm means explains about the microscopic particles..
KRANTHI
nope name of d sun god
Antares
why the mercury used in thermometers?
jyotirmayee
Ali brother ur exactly spelling is wrong,,,,,
jyotirmayee
why the colour of tube light white?
jyotirmayee
why the mouth became red colour ,,by the regular eating of leaf called ,,betel combining with areca?
jyotirmayee
quantum mechanics is the study of the photon the light particle
Agrim
all formula for calculate specific latent heat of any substance
it is the product of electric charges and distance between the two charges
Shikhar
mishra true thanks dia
Ssempala
product of separation of the poles, the rest shikhar got is right
Brad
brad is separation and distance ,are they different?
Ssempala
What is actually a dipole? I know charge separated by a certain distance.... but what does that really mean? what happens in a dipole? why are the charge of same magnitude?
Monalisa
Dipoles forming as a result of the unbalanced distribution of electrons in asymmetrical molecules