THIS WAS MOVED FROM ANOTHER FORUM, SO THERE IS NO TEMPLATE. HOWEVER, THE OP DID SHOW SOME EFFORT Hello, I have been having troubles beginning these two problems given for exam prep. Was wondering if anyone could give guidance on where to begin. Problem 1: A cylinder with adiabatically isolated walls is closed at both ends and is divided into two volumes by a frictionless piston that is also thermally insulating. Initially, the volume, temperature and pressure of the ideal gas on each side of the cylinder are equal at V0, T0 and p0, respectively. A heating coil, inserted in the right hand volume, is used to heat slowly the gas on that side until the pressure reaches (64/27) p0 = 2.37 p0. If the heat capacity CV of the gas is independent of temperature, and Cp/CV = 1.5, (a) find first the entropy change of the gas on the left (no calculation needed for this step!), (b) then calculate the final left–hand volume in terms of V0, (c) and finally, calculate the final temperature in terms of T0 on the left hand side. For this problem, I am unsure of (b). For (a) I determined that since the system is adiabatically isolated, and the piston is also thermally insulating, no heat can enter or exit the volume on the left. Because of this the change in entropy is equal to zero since Q = 0. (b) is slightly confusing for me since I don't where to begin. If we heat up the RHS with the heating coil and then shut it off when pressure reaches 2.37p0, we are unsure if the volume has remained the same while the temperature and pressure increase. I figure part (c) requires part (b) to solve so I haven't gotten this far. Problem 2: A column of water contains fine metal particles of radius 20 nm, which are in thermal equilibrium at 25°C. If there are 1000 such particles per unit volume at a given height h0 in the water column, how many particles would be found in the same volume 1.0 mm higher than h0? The density of the used metal is ρ = 20.0 g/cm3. For this problem I have not made any progress on it as I have no clue what equations pertain to this problem and was hoping someone could lead me in the right direction. Thanks everyone!