Question

-explain evaporation in terms of the Maxwellian velocity distribution.

-How do the degrees of freedom in the equipartition of energy relate to motion in monatomic and diatomic particles?

- What happens to ideal gases during an adiabatic compression or expansion.

- When does entropy change in calorimetry(like when does it increase, decrease or remain constant)?

- What is true for reversible, adiabatic processes in terms of change in entropy, internal energy, heat and work?

Answer 1

1.the atoms or molecules of the gas do not really interact with each other except through collisions.we can think gas as a collection of tiny little billiard balls heating each other.the constant collision results in a spread in speed,i.e some balls have large speed and some have small speed.in real gases at equilibrium there is a distribution in the speed,this distribution is called maxwell boltzman distribution and it depends on temperature.

Molecules approaching the boundary of a liquid are trapped back into the liquid by the surface tension. The very fast molecules may be able to penetrate the surface barrier and escape the liquid altogether. The more surface available,the faster the rate of escape. The rate also increases as the temperature increases because of the boosting of molecules to higher speeds. We may distinguish two sorts of evaporation. In liquids with a relatively small surface area, the liquid absorbs heat from the surroundings to keep the temperature of the liquid fixed as the faster molecules escape. The absorbed heat speeds up some molecules, restoring the original Maxwell-Boltzmann distribution. The total number of molecules in the liquid decreases, but the distribution—which depends only on temperature—remains the same. In the second sort of evaporation, the surface area is relatively large. Thus, the faster molecules leave the surface rapidly enough that the liquid cannot absorb enough heat to restore the original distribution.

2.The equipartition theorem states that energy is shared equally amongst all energetically accessible degrees of freedom of a system. Specifically, it states that each quadratic degree of freedom will, on average, possess an energy ½kT. A ‘quadratic degree of freedom’ is one for which the energy depends on the square of some property. Consider the kinetic and potential energies associated with translational, rotational and vibrational energy. Translational degrees of freedom K = ½mv2 Rotational degrees of freedom K = ½Iω2 Vibrational degrees of freedom K = ½mv2 V = ½kx2 These three types of degrees of freedom all have a quadratic dependence on the velocity (or angular velocity in the case of rotation) and therefore all follow the equipartition theorem. The Molecules of monoatomic gas can move in any direction in space so it can have three independent motions and hence 3 degree of freedom (all translational). A molecule of diatomic gas has five degrees of freedom (3tanslational and 2 rotational).1 degree of freedom is added at high temperature(1 vibrational).

3.If the gas is allowed to expand quasi-statically under these so called adiabatic conditions then it does work on its environment, and, hence, its internal energy is reduced, and its temperature increases.

4. a reversible process is a process whose direction can be "reversed" by inducing infinitesimal changes to some property of the system via its surroundings, with no increase in entropy,whereas an irreversible process increases the entropy of the universe,because entropy is a state function.