The Tait equation for liquids is written for an isotherm as: $V=V_{0}\left(1-\frac{A P}{B+P}\right)$ where V is molar or specific volume, $V_0$ is the hypothetical molar or specific volume at zero pressure, and A and B are positive constants. Find an expression for the isothermal compressibility consistent with this equation.

A system comprised of chloroform, 1,4-dioxane, and ethanol exists as a two-phase vapor/liquid system at $50^\circ C$ and 55 kPa. After the addition of some pure ethanol, the system can be returned to two-phase equilibrium at the initial T and P. In what respect has the system changed, and in what respect has it not changed?

The yield in pounds from a day’s production is normally distributed with a mean of 1500 pounds and a variance of 10,000 pounds squared. Assume that the yields on different days are independent random variables. (a) What is the probability that the production yield exceeds 1400 pounds on each of 5 days? (b) What is the probability that the production yield exceeds 1400 pounds on none of the next 5 days?

Calculate the reversible work done in compressing $1(ft)^3$ of mercury at a constant temperature of $32(^\circ F)$ from 1(atm) to 3000(atm). The isothermal compressibility of mercury at $32(^\circ F)$ is: $\kappa /(\mathrm{atm})^{-1}=3.9 \times 10^{-6}-0.1 \times 10^{-9} P /(\mathrm{atm})$

For liquid water the isothermal compressibility is given by: $\kappa=\frac{C}{V(P+b)}$ where c and b are functions of temperature only. If 1 kg of water is compressed isothermally and reversibly from 1 to 500 bar at $60^\circ C,$ how much work is required? At $60^\circ C,$ b = 2700 bar and $c=0.125 \mathrm{cm}^{3} \cdot \mathrm{g}^{-1}$

Find the area of the surface generated when the given curve is revolved about the given axis. $y=x^{3 / 2}-\frac{x^{1 / 2}}{3}$, for $1 \leq x \leq 2$; about the x-axis

Evaluate the expression. $\frac{|-4|}{-4}$

A renowned laboratory reports quadruple-point coordinates of 10.2 Mbar and $24.1^\circ C$ for four-phase equilibrium of allotropic solid forms of the exotic chemical $\beta -miasmone.$ Evaluate the claim.

Comment on the feasibility of cooling your kitchen in the summer by opening the door to the electrically powered refrigerator.

The state of an ideal gas with $C_P = (5/2)R$ is changed from P = 1 bar and $V_{1}^{t}=12 \mathrm{m}^{3}$ to $P_2 = 12$ bar and $V_{2}^{t}=1 \mathrm{m}^{3}$ by the following mechanically reversible processes: (a) Isothermal compression. (b) Adiabatic compression followed by cooling at constant pressure. (c) Adiabatic compression followed by cooling at constant volume. (d) Heating at constant volume followed by cooling at constant pressure. (e) Cooling at constant pressure followed by heating at constant volume. Calculate $Q, W, \Delta U^{t}, \text { and } \Delta H^{t}$ for each of these processes, and sketch the paths of all processes on a single PV diagram.

Gas at constant T and P is contained in a supply line connected through a valve to a closed tank containing the same gas at a lower pressure. The valve is opened to allow flow of gas into the tank, and then is shut again. (a) Develop a general equation relating $n_1$ and $n_2,$ the moles (or mass) of gas in the tank at the beginning and end of the process, to the properties $U_1$ and $U_2,$ the internal energy of the gas in the tank at the beginning and end of the process, and H', the enthalpy of the gas in the supply line, and to Q, the heat transferred to the material in the tank during the process.(b) Reduce the general equation to its simplest form for the special case of an ideal gas with constant heat capacities. (c) Further reduce the equation of (b) for the case of $n_1 = 0.$ (d) Further reduce the equation of (c) for the case in which, in addition, Q = 0. (e) Treating nitrogen as an ideal gas for which $C_P = (7/2)R,$ apply the appropriate equation to the case in which a steady supply of nitrogen at $25^\circ C$ and 3 bar flows into an evacuated tank of $4 m^3$ volume, and calculate the moles of nitrogen that flow into the tank to equalize the pressures for two cases: 1. Assume that no heat flows from the gas to the tank or through the tank walls. 2. Assume that the tank weighs 400 kg, is perfectly insulated, has an initial temperature of $25^\circ C,$ has a specific heat of $0.46 \mathrm{kJ} \cdot \mathrm{kg}^{-1} \cdot \mathrm{K}^{-1}$ and is heated by the gas so as always to be at the temperature of the gas in the tank.

Water at $28^\circ C$ flows in a straight horizontal pipe in which there is no exchange of either heat or work with the surroundings. Its velocity is $14 m\cdot s^{−1}$ in a pipe with an internal diameter of 2.5 cm until it flows into a section where the pipe diameter abruptly increases. What is the temperature change of the water if the downstream diameter is 3.8 cm? If it is 7.5 cm? What is the maximum temperature change for an enlargement in the pipe?

Fifty (50) kmol per hour of air is compressed from $P_1 = 1.2$ bar to $P_2 = 6.0$ bar in a steady-flow compressor. Delivered mechanical power is 98.8 kW. Temperatures and velocities are:

$$\begin{array}{ll}{T_{1}=300 \mathrm{K}} & {T_{2}=520 \mathrm{K}} \\ {u_{1}=10 \mathrm{m} \cdot \mathrm{s}^{-1}} & {u_{2}=3.5 \mathrm{m} \cdot \mathrm{s}^{-1}}\end{array}$$

Estimate the rate of heat transfer from the compressor. Assume for air that $C_{P}=\frac{7}{2} R$ and that enthalpy is independent of pressure.

A closed, nonreactive system contains species 1 and 2 in vapor/liquid equilibrium. Species 2 is a very light gas, essentially insoluble in the liquid phase. The vapor phase contains both species 1 and 2. Some additional moles of species 2 are added to the system, which is then restored to its initial T and P. As a result of the process, does the total number of moles of liquid increase, decrease, or remain unchanged?