2.185. A saturated water vapour is contained in a cylindrical vessel under a weightless piston at a temperature t = 100 °C. As a result of a slow introduction of the piston a small fraction of the vapour Δm = 0.70 g gets condensed. What amount of work was performed over the gas? The vapour is assumed to be ideal, the volume of the liquid is to be neglected.
2.186. A vessel of volume V = 6.0 l contains water together with its saturated vapour under a pressure of 40 atm and at a temperature of 250 °C. The specific volume of the vapour is equal to V_{v}' = 50 l/kg under these conditions. The total mass of the system watervapour equals m = 5.0 kg. Find the mass and the volume of the vapour.
2.191. One gram of saturated water vapour is enclosed in a thermally insulated cylinder under a weightless piston. The outside pressure being standard, m = 1.0 g of water is introduced into the cylinder at a temperature t_{0} = 22 °C. Neglecting the heat capacity of the cylinder and the friction of the piston against the cylinder's walls, find the work performed by the force of the atmospheric pressure during the lowering of the piston.
2.192. If an additional pressure Δp of a saturated vapour over a convex spherical surface of a liquid is considerably less than the vapour pressure over a plane surface, then Δp = (ρ_{v}/ρ_{l})2α/r, where ρ_{v} and ρ_{l} are the densities of the vapour and the liquid, α is the surface tension, and r is the radius of curvature of the surface. Using this formula, find the diameter of water droplets at which the saturated vapour pressure exceeds the vapour pressure over the plane surface by η = 1.0% at a temperature t = 27 °C. The vapour is assumed to be an ideal gas.
2.196. Find the internal pressure p_{i} of a liquid if its density ρ and specific latent heat of vaporization q are known. The heat q is assumed to be equal to the work performed against the forces of the internal pressure, and the liquid obeys the Van der Waals equation. Calculate p_{i} in water.
2.197. Demonstrate that Eqs. (2.6a) and (2.6b) are valid for a substance, obeying the Van der Waals equation, in critical state.
2.198. Calculate the Van der Waals constants for carbon dioxide if its critical temperature T_{cr} = 304 K and critical pressure p_{cr} = 73 atm.
2.200. Write the Van der Waals equation via the reduced parameters π, ν, and τ, having taken the corresponding critical values for the units of pressure, volume, and temperature. Using the equation obtained, find how many times the gas temperature exceeds its critical temperature if the gas pressure is 12 times as high as critical pressure, and the volume of gas is equal to half the critical volume.
2.210. Find the pressure of saturated vapour as a function of temperature p(T) if at a temperature T_{0} its pressure equals p_{0}. Assume that: the specific latent heat of vaporization q is independent of T, the specific volume of liquid is negligible as compared to that of vapour, saturated vapour obeys the equation of state for an ideal gas. Investigate under what conditions these assumptions are permissible.
