Physical Chemistry - Magnetic Spin System - Work Capacities - Mathematics Assignment Help

Assessment Task:

Physical Chemistry - Magnetic Spin System - Work Capacities - Mathematics Assignment Help 

Overview 

(30) Two particles with masses m1 and m2 are moving with initial speeds v1 and v2, respectively. They collide with each other, and then continue along. None of the energy is lost to other kinds of motion, and there are no external forces working on the particles (i.e. the potential energy can be set to zero). Use conservation of energy and linear momentum to find the speeds v1’ and v2’ or the particles after the collision.
2. (30) If a magnetic spin system has an energy obeying the equation

Where E0 and T0 are constants, find the temperature (in terms of T0) at which the heat capacity Cv reaches its maximum value, given that the maximum is the only critical point. Graph the Cv term vs temperature.
3. (20) The heat capacity gives the heat transfer per unit temperature change  and we define these at constant V or at constant P. In the same way we can define “work capacities” at constant T or S, BT and BS by 
Find an expression for BT in terms of BS, replacing any remaining partial derivatives with α, V, CP, and T.
4. (30) Find the isothermal compressibility kT for a gas obeying the virial expansion in terms of P, T, V, B2. Demonstrate that the answer makes sense in terms of the ideal limit, non-ideality in for He and H2, and non-ideality for other gases.
5. (20) P-V plots for three different expansion scenarios are shown in the figure below. Reproduce the graphs for a) reversible and isothermal, b) irreversible and isothermal,
and c) reversible and adiabatic. Discuss how the graphs demonstrate the work done in each case.

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