Suppose you have a gas that obeys the following modified van der Waals equation: P(V-nb)=nRT   a)  In 1–2 sentences, provide a physical interpretation for this equation. HINT:  Compare this with the actual van der Waals equation. What does the missing term represent? b)  For a gas obeying this modified van der Waals equation, derive an expression for the work done by a reversible and isothermal change in volume. c)  For this modified van der Waals equation (with n and b as constants), find the following two partial derivatives for i and ii

Consider 1.2 moles of a diatomic gas that expands adiabatically from an initial pressure of 5.0 x 10^5  Pa and a temperature of 400 K to a final pressure of 1.0 x 10^5  Pa.  a) Find the final temperature. b) Find the final volume. c) Find the work done by the gas. d) Find the change in internal energy of the gas.

Hydrogen behaves as an ideal gas at temperatures greater than 200 K and at pressures less than 50 atm. Suppose 6.00 mol hydrogen is initially contained in a 100-L vessel at a pressure of 2.00 atm. The average molar heat capacity of hydrogen at constant pressure, c, is 29.3 J K-' mol-1 in the temperature range of this problem. The gas is cooled reversibly at constant pressure from its initial state to a volume of 50.0 L. Calculate the following quantities for this process. (a) Temperature of the gas in the final state, T2 (b) Work done on the gas, w, in joules (c) Internal energy change of the gas, AU, in joules (d) Heat absorbed by the gas, q, in joules

Consider the free, isothermal (constant T) expansion of an ideal gas. "Free" means that the external force is zero, perhaps because a stopcock has been opened and the gas is allowed to expand into a vacuum. Calculate AU for this irreversible process. Show that q sion is also adiabatic (q = 0) for an ideal gas. This is analogous to a classic experiment first performed by Joule. 0, so that the expan-