The heat of fusion of ice at the standard melting point $\left(0^{\circ} \mathrm{C}\right)$ is $6.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Determine the heat of fusion at $-10^{\circ} \mathrm{C}$ using data from Appendix 2.

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

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

Consider the following reaction at 298 K:

$$2 \mathrm{H}_2(g)+\mathrm{O}_2(g) \longrightarrow 2 \mathrm{H}_2 \mathrm{O}(l), \Delta H^{\circ}=-571.6 \mathrm{~kJ} / \mathrm{mol}$$

Calculate $\Delta S_{\text {sys }}, \Delta S_{\text {sur }}$, and $\Delta S_{\text {univ }}$ for the reaction.

Calculate $\Delta G^{\circ}$ for the melting of water: $\mathrm{H}_2 \mathrm{O}(\mathrm{s}) \longrightarrow$ $\mathrm{H}_2 \mathrm{O}(l)$ at $-10.0^{\circ} \mathrm{C}$
assuming that the enthalpy and entropy of fusion are constant over the temperature range.

At the critical point, both the slope $\left[\left(\frac{\partial p}{\partial v}\right)_\tau\right]$ and the curvature $\left[\left(\frac{2}{\partial v^2}\right)_{\text {f }}\right]$ along the critical isotherm are zero. Use these conditions to derive Equations 6.1, 6.2 and $6.3$ for the critical volume, pressure, and temperature of a system obeying the van der Waals equation of state (Equation 5.42).

The enthalpy of vaporization is found to decrease with increasing temperature for a certain substance. What information does this give you about the relative properties of the liquid and vapor phases?

The molar enthalpies of fusion and vaporization of water at $298 \mathrm{~K}$ are $6.01$ and $44.01 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. Use these values to estimate the molar enthalpy of sublimation of ice.

The molar enthalpies of fusion and sublimation of molecular iodine are $15.27$ and $62.30 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. Estimate the molar heat of vaporization of liquid iodine.

How much heat (in kJ) is needed to convert $866 \mathrm{~g}$ of ice at $-10^{\circ} \mathrm{C}$ to steam at $126^{\circ} \mathrm{C}$ ? (The specific heat capacities of ice and steam are $2.03$ and $1.99 \mathrm{~J} \mathrm{~g}^{-1}$ ${ }^{\circ} \mathrm{C}^{-1}$, respectively.)

The ends of a chain lie in piles at A and C. When released from rest at time t = 0, the chain moves over the pulley at B, which has a negli-gible mass. Denoting by L the length of chain connecting the two piles and neglecting friction, determine the speed v of the chain at time t.

Seawater has density 1025 kg/m^3 and flows in a velocity field

$$v = yi + xj,$$

where x, y, and z are measured in meters and the components of v in meters per second. Find the rate of flow outward through the hemisphere

$$x^2+y^2+z^2=9, z≥0.$$

Use Green’s Theorem to evaluate the line integral along the given positively oriented curve. integral through C y^4dx+2xy^3dy, C is the ellipse x^2+2y^2=2

Evaluate the line integral, where C is the given curve. integral through C (x^2+y^2+z^2)ds, C: x=1, y=cos2t, z=sin2t, 0<=t<=2pi

Calculate the amount of heat (in $\mathrm{kJ}$ ) required to convert $74.6 \mathrm{~g}$ of water to steam at $100^{\circ} \mathrm{C}$.