Find the entropy change of an ideal gas and of a van der Waals gas in case of isothermal expansion in which the volume increases by a factor alpha. Also, find the entropy change in case of a free expansion in which the volume increases by a factor alpha.

In case of the free expansion of the van der Waals gas, find the temperature change.

If we let a gas expand slowly, then it will perform work. If we know the internal energy as a function of volume and temperature and we keep the temperature the same during the expansion, then we know by how much the internal energy has changed during the expansion. We also know how much work the gas has performed, so we know the heat that the gas has absorbed. If we divide this heat by the temperature we get the entropy increase. In case of an ideal gas the internal energy does not depend on the volume for fixed temperature. So, the heat absorbed by the gas is equal to the work performed by the gas. For the van der Waals gas this is not true and we need to use the internal energy function to compute the entropy change.

In part b) we can use that in case of free expansion no heat is absorbed and no work is performed, so the internal energy stays constant. In case of an ideal gas we then know that means that the temperature stays constant (I'll derive that later). But then you get the same result as in a) for the entropy because temperature and volume are the same in the end state. In case of the van der Waals gas the temperature will change. We can use the internal energy as a function of temperature and volume to find by how much the temperature will change.

So, we see that to solve the problems we need to find the internal energy change in terms of changes in temperature and volume. I derived this for another problem a few days ago, so I have included that derivation here:

The fundamental thermodynamic relation expresses dU in terms of dS and dV

dU = T dS - P dV (1)

If we want to consider U as a function of T and V, then all we need to do is rewrite this in terms of dT and dV. We substitute:

dS = dS/dT dT + dS/dV dV (2)

Here the derivatives are partial derivatives, the derivative ...

A certain gas obeys the vanderWaals equation with a = 0.76 (m^6) Pa/(mol^2). Its volume is found to be 4.00 x 10-4 (m^3)/mol at 288 K and 4.0 MPa. From this information, calculate the vanderWaals constant b. What is the compression factor for this gas at the prevailing temperature and pressure?

Express the vanderWaals equation of state as a virial expansion in powers of 1/(V_m), and obtain expressions for B and C in terms of the parameters a and b. The expansion you will need is (1 - x)^(-1) = 1 + x + (x^2) + ...
Measurements on argon gave B = -21.7 (cm^3)/mol and C = 1200 (cm^6)/(mol^2) for the virial coeffici

Calculate the molar volume of chlorine gas at 350 K and 2.30 atm using (a) the perfect gas law and (b) the vanderWaals equation.
Use the answer to (a) to calculate a first approximation to the correction term for attraction, and then use successive approximations to obtain a numerical answer for part (b).

7.4
Consider n moles of a VanderWaalsgas. Show that (dU/dV)_T = n^2a/V^2. Hence show that the internal energy is
U = the integral from zero to T of C_vdT - an^2/V + U0
where U0 is a constant. {Hint: Express U = U(T,V)}.
7.5
As in the previous question, consider n moles of VanderWaalsgas. Show that
(a) S = the in

The critical point is the unique point on the original vanderWaals isotherms (before the Maxwell construction) where both the first and second derivatives of P with respect to V (at fixed T) are zero. Use this fact to show that:
V_c = 3Nb, P_c = (1/27) (a/b2), kT_c = (8/27) (a/b).

In an industrial process, nitrogen has to be heated to 500K at constant volume. If it enters the system at 300 K and 100 atm, what pressure does it exert at its final working temperature? Treat it as a vanderWaalsgas. Assume the volume is 1 m^3 (where "^" means "to the exponent").

The equation of state of one mole of a vanderWaalsgas is given by
(P+a/(v^2))(V-b) = RT
with a and b are constants.
a) Calculate the work W in an isothermal reversible process when volume changes from V1 to V2.
b) Using the energy equation, show that (du/dV) = a/v^2
c) Calculate the change in internal energy U in th

1. Calculate the average kinetic energy of the N2 molecules in a sample of N2 gas at
273K and at 546K.
2. Consider separate 1.0 L gaseous samples of H2, Xe, Cl2 and O2 at STP.
a) Rank gases in increasing kinetic energy.
b) Rank gases in increasing velocity.
c) How can separate 1.0 L samples of H2 and O2 have the same aver

Lidocaine is thought to bind to receptors in its methylated form.
identify in writting the atoms or groups in the compound that could be involved in its binding to a receptor via- hydrogen bonding (1 example)
an ionic interaction
give the 2 types of functional groups that need to be present in the receptor s