A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of

$$\theta$$

with respect to the vertical. (a) Derive an expression for the magnitude a of the acceleration of the van in terms of the angle

$$\theta$$

and the magnitude g of the acceleration due to gravity. (b) Find the acceleration of the van when

$$\theta = 10.0 ^ { \circ }$$

(c) What is the angle

$$\theta$$

when the van moves with a constant velocity?

One kmol of argon at $300 \mathrm{~K}$ is initially confined to one side of a rigid, insulated container divided into equal volumes of $0.2 \mathrm{~m}^3$ by a partition. The other side is initially evacuated. The partition is removed and the argon expands to fill the entire container. Using the van der Waals equation of state, determine the final temperature of the argon, in K. Repeat using the ideal gas equation of state.

Solve the previous problem using (a) ideal gas and (b) van der Waal's EOS.

Show that the work required for the reversible and isothermal expansion of $n$ moles of a van der Waals gas (Equation $5.42$ ) from an initial volume $V_1$ to a final volume $V_2$ is given by

$$w=n R T \ln \frac{V_1-n b}{V_2-n b}+a n^2\left(\frac{1}{V_1}-\frac{1}{V_2}\right)$$

Determine the pressure of R-410a at 100 F, v = 0.2 ft3/lbm using ideal gas and the van der Waal EOS.

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¿Adónde van para hacer la tarea y cómo van a ir a ese lugar?

(a) For a van der Waals gas, $\pi_T=a / V_{\mathrm{m}}^2$. Calculate $\Delta U_{\mathrm{m}}$ for the isothermal expansion of nitrogen gas from an initial volume of $1.00 \mathrm{dm}^3$ to $24.8 \mathrm{dm}^3$ at $298 \mathrm{~K}$. What are the values of $q$ and $w$ ?

(b) Repeat the previous exercise for argon, from an initial volume of $1.00 \mathrm{dm}^3$ to $22.1 \mathrm{dm}^3$ at $298 \mathrm{~K}$.

Describe cómo van vestidas estas personas.

Distinguish between adhesive forces and cohesive forces.

One kmol of argon at $300 \mathrm{~K}$ is initially confined to one side of a rigid, insulated container divided into equal volumes of $0.2 \mathrm{~m}^3$ by a partition. The other side is initially evacuated. The partition is removed and the argon expands to fill the entire container. Using the van der Waals equation of state, determine the final temperature of the argon, in $\mathrm{K}$. Repeat using the ideal gas equation of state.

Use the van der Waals equation to calculate the pressure in bars exerted by 45 grams of propane, $\mathbf{C}_{3} \mathbf{H}_{8}(g)$, confined to a 2.2-liter container at $300.0^{\circ} \mathrm{C}$. Compare your answer with the pressure calculated using the ideal-gas equation.

Show that for a van der Waals gas,

$$C_{p, \mathrm{~m}}-C_{V, \mathrm{~m}}=\lambda R \quad \frac{1}{\lambda}=1-\frac{\left(3 V_{\mathrm{r}}-1\right)^2}{4 V_{\mathrm{r}}^3 T_{\mathrm{r}}}$$

and evaluate the difference for xenon at $25^{\circ} \mathrm{C}$ and $10.0 \mathrm{~atm}$.

Show that the van der Waals equation can be written as a cubic equation in the compressibility factor involving the reduced pressure and reduced temperature as $Z^{3}-\left(\frac{P_{r}}{8 T_{r}}+1\right) Z^{2}+\left(\frac{27 P_{r}}{64 T_{r}^{2}}\right) Z-\frac{27 P_{r}^{2}}{512 T_{r}^{3}}=0$.

Corrige los siguientes vulgarismo. A la derecha verás la versión correcta. Cúbrela mientras hagas el ejercicio.

Lo van a inspectar. - Lo van a inspeccionar.