A binary mixture of mole fraction $z_1$ is flashed to conditions T and P. For one of the following, determine the equilibrium mole fractions $x_1$ and $y_1$ of the liquid and vapor phases formed, the molar fraction $\mathcal{V}$ of the vapor formed, and the fractional recovery $\mathcal{R}$ of species 1 in the vapor phase (defined as the ratio for species 1 of moles in the vapor to moles in the feed). Assume that Raoult’s law applies. (a) Acetone(1)/acetonitrile(2), $z_1$ = 0.75, T = 340 K, P = 115 kPa. (b) Benzene(1)/ethylbenzene(2), $z_1 = 0.50,$ $T = 100^\circ C,$ P = 0.75(atm). (c) Ethanol(1)/1-propanol(2), $z_1$ = 0.25, T = 360 K, P = 0.80(atm).  (d) 1-Chlorobutane(1)/chlorobenzene(2), $z_1$ = 0.50, $T = 125^\circ C,$ P = 1.75 bar

Solve the following initial value problems. $y^{\prime}(x)=3 x^{2}-3 x^{-4}, y(1)=0$

Two nonconducting tanks of negligible heat capacity and of equal volume initially contain equal quantities of the same ideal gas at the same T and P. Tank A discharges to the atmosphere through a small turbine in which the gas expands isentropically; tank B discharges to the atmosphere through a porous plug. Both devices operate until discharge ceases. (a) When discharge ceases, is the temperature in tank A less than, equal to, or greater than the temperature in tank B? (b) When the pressures in both tanks have fallen to half the initial pressure, is the temperature of the gas discharging from the turbine less than, equal to, or greater than the temperature of the gas discharging from the porous plug? (c) During the discharge process, is the temperature of the gas leaving the turbine less than, equal to, or greater than the temperature of the gas leaving tank A at the same instant? (d) During the discharge process, is the temperature of the gas leaving the porous plug less than, equal to, or greater than the temperature of the gas leaving tank B at the same instant? (e) When discharge ceases, is the mass of gas remaining in tank A less than, equal to, or greater than the mass of gas remaining in tank B?

A gardener wants to replace the fence along the perimeter of her garden. How much new fencing will be required?

Write the expression with only one exponent. Use parentheses.

$$\left(a^{5}\right)\left(b^{5}\right)\left(a^{0}\right)$$

Ballo Brothers is a partnership owned by Abdalla Ballo and Rashad Ballo. Information from Ballo Brothers' general ledger and income statement is given below.

$$\begin{matrix} \text{Net income for the month ended October 31} & \text{\$ 62,500.00}\\ \text{Abdalla Ballo, Capital October 1 balance} & \text{40,000.00}\\ \text{Rashad Ballo, Capital October 1 balance} & \text{36,000.00}\\ \text{Abdalla Ballo, Drawing October 31 balance} & \text{1,500.00}\\ \text{Rashad Ballo, Drawing October 31 balance} & \text{1,900.00}\\ \end{matrix}$$

Prepare a distribution of net income statement for Ballo Brothers. Net income or loss is to be distributed $60\%$ to Abdalla Ballo and $40\%$ to Rashad Ballo.

In a desuperheater, liquid water at 3100 kPa and $50^\circ C$ is sprayed into a stream of superheated steam at 3000 kPa and $375^\circ C$ in an amount such that a single stream of saturated-vapor steam at 2900 kPa flows from the desuperheater at the rate of $15 kg \cdot s^{−1}.$ Assuming adiabatic operation, what is the mass flow rate of the water? What is $\dot{S}_{G}$ for the process? What is the irreversible feature of the process?

Construct a grammar that shows that $L=\left\{(a b)^{n} | n \in \mathbf{N}\right\}$ is a terminal language.

Find the missing value.

$$\begin{array}{|c|c|c|}\hline & & {\text { Scientific }} \\ & {\text { Standard Notation }} & {\text { Notation }} \\ \hline \text { Dog } & {10} & {\square} \\ \hline\end{array}$$

The infinite heat reservoir is an abstraction, often approximated in engineering applications by large bodies of air or water. Apply the closed-system form of the energy balance to such a reservoir, treating it as a constant-volume system. How is it that heat transfer to or from the reservoir can be nonzero, yet the temperature of the reservoir remains constant?

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they be found in a table. $\int \frac{\cos x}{\sin ^{2} x+2 \sin x} d x$

In comparing the performance of a real cycle with that of a Carnot cycle, one has in principle a choice of temperatures to use for the Carnot calculation. Consider a vapor-compression refrigeration cycle in which the average fluid temperatures in the condenser and evaporator are $T_H$ and $T_C,$ respectively. Corresponding to $T_H$ and $T_C,$ the heat transfer occurs with respect to surroundings at temperature $T_{\sigma_{H}} \text { and } T_{\sigma_{C}}.$ Which provides the more conservative estimate of $\omega_{\text {Carnot }}:$ a calculation based on $T_H$ and $T_C,$ or one based on $T_{\sigma_{H}} \text { and } T_{\sigma_{C}} ?$

Insert a dash or dashes where necessary. My father has typical middle-class values he believes in hard work, family life, education, and property ownership although he was born very poor.

What items are included in real property?