what is enthalpy and entropy?
Answers
Entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system.
Enthaply
Consider an ideal gas in a closed vessel. The energy it contains is a measured by internal energy ‘u’, which is a function of the temperature of the gas.
Now if the gas is forced out of the vessel, the gas has to do some work against the atmosphere at pressure P. It does this work by pushing the atmosphere along a boundary which encloses the volume V, which the gas now occupies.
So apart from internal energy U, the gas has another component energy, which is the flow work done given by PV. So the total energy the gas contains is given by U+PV. For the sake of convenience, both these are clubbed together in one term, called ‘enthalpy’. Enthalpy ‘H’ is given by -
H = U + PV
U is a pure function of temperature, given by U = m*C
For an ideal gas, we have ideal gas relation PV = mRT , R is the characteristic gas constant.
For an ideal gas, enthalpy is a pure function of temperature
Entropy
Long before Boltzmann, when the idea of atoms was not widely accepted, heat was thought of as a fluid called caloric, which flowed from a body at high temperature to a body at lower temperature.
From that point of view, entropy was defined in the following way -
ds = δ δ Q/T
Q flowed into a body at a temperature T, it led to an increase of the entropy of the system. But the above relation was only true if the change was carried out reversibly. For an irreversible change, the following was found to hold good -
ds >
δ
δ
Q/T
ds =
δ
δ
Q/T + I
Entropy change has two parts which contribute to it -
Entropy transfer - Occurs in the form of heat transfer and or mass transfer
Q/T) i.e. entropy transfer may be positive, negative or 0 depending on direction of flow.
For any process to occur to occur spontaneously, it is a necessary condition that the entropy of the system undergoing the process should increase. If the entropy decreases, then that process cannot occur spontaneously. It needs some work/ energy to be pumped in in order for the process to occur. And this usually is dependant on the entropy transfer
δ
δ
Q/T, as it is usually much greater than the entropy generated.
Entropy was thought of as a measure of how much energy was in a system and how it was distributed.
What is a microstate?
When you are looking at matter not as a continuum , but a collection of particles, we can define a microstate. A ‘microstate’ refers to a description of the system which relies on the states of each element of the system. Applied to a thermodynamic system, each microstate Mi
i
i
of the system is a set of positions and velocities which describe the position and velocity of each particle. All these microstates come together to define macrostates of system such as pressure, temperature etc.
Relating this to the example, when the people were in the small room, they had less freedom, and when the door opened to the other room, they had more freedom. Same with energy in a high temperature body which comes in contact with a lower temperature body. It has a chance to be more dissipated, so it does.
Energy will always go from a state where it has access to fewer microstates, to a state where it has more microstates. This is because when it has more microstates accessible, it can be arranged in more ways. When it can be arranged in more ways, the probability of finding it in that state increases. So the only reason for energy/atoms/mass to flow, is that you have a higher probability of finding it in that dissipated state than being grouped in a corner.
When you have a high temperature body like object 1, it has a lot of energy within it compared to the lower energy object 2.
Now when the two are brought in contact, the random motion of the molecules take energy in both directions, from hot to cold and from cold to hot. Its just that the transfer from hot to cold is way more than that from cold to hot body. Now the energy in object 1 has more microstates in object 2 which it has access to, so it flows there and it gets evenly distributed, because mathematically, that’s what has the highest probability of occurring.
Consider you have a box of different black and white balls, that you then shake vigorously. When you open it, you expect to see them well mixed up. But why? There is a small probability that all the balls will separate, and all the white balls will go to one side, and all the black balls will go to the other. However, the number of ways in which they can be mixed up is much much greater than the the number of ways they can be separated. So the probability of them being mixed up is much greater than them being separated. So this is what you see. Whichever has the highest probability, you see that as the result (balls being mixed) .
From this microstate point of, Boltzmann gave the following relation to define entropy -
S = k*lnW where W represents the microstates accessible. The more microstates that are accessible, the greater the entropy.
k is the Boltzmann’s constant with a value of 1.38064852 × 10-23
kgm2s2K