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# 物理代写|热力学代写Thermodynamics代考|MAE204 Thermodynamics Problems

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## 物理代写|热力学代写Thermodynamics代考|Thermodynamics Problems

Derive an expression for the volumetric expansion coefficient $(\alpha)$ for an ideal gas; $\alpha$ is given by: $\left(\alpha=(1 / V)(\partial V / \partial T)_p\right.$.

Derive an expression for the isothermal compressibility $\left(\kappa_{\mathrm{T}}\right)$ for an ideal gas; $\kappa_{\mathrm{T}}$ is given by: $\kappa_{\mathrm{T}}=(-1 / V)(\partial V / \partial p)_T$.
First Law

For an ideal gas, the following relation holds: $(\partial U / \partial V)_T=0$. Derive the following relationships from this expression: (a) $(\partial U / \partial p)_T=0$; (b) $(\partial H / \partial V)_T=0$; (c) $(\partial H / \partial p)_T=0 ;$ (d) $(\partial T / \partial p)_H=0$.

Show that $C_{\mathrm{p}, \mathrm{m}}-C_{\mathrm{v}, \mathrm{m}}=R$ for an ideal gas.

The heat capacities at constant pressure for $\mathrm{CHCl}3$ are $118 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}$ (liquid) and $71(\mathrm{~K} \mathrm{~mol})^{-1}$ (gas). The evaporation enthalpy $\left(\Delta H{\text {vap }, \mathrm{m}}\right)$ at $60{ }^{\circ} \mathrm{C}$ is $29.20 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate $\Delta H_{\text {vap, }, \mathrm{m}}$ at $20^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C}$.

Calculate $\Delta H^0$ and $\Delta U^0$ for hydrogenation of acetylene to ethylene at $25^{\circ} \mathrm{C}$ and 1 bar based on $\Delta H^0$ data of the following reactions:
\begin{aligned} &\mathrm{H}_2(g)+1 / 2 \mathrm{O}_2(g) \rightarrow \mathrm{H}_2 \mathrm{O}(l) \Delta H^0{ }_1=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \ &\mathrm{C}_2 \mathrm{H}_2(g)+2 \frac{1}{2} \mathrm{O}_2(g) \rightarrow \mathrm{H}_2 \mathrm{O}(l)+2 \mathrm{CO}_2(g) \Delta H_2^0=-1300 \mathrm{~kJ} \mathrm{~mol}^{-1} \ &\mathrm{C}_2 \mathrm{H}_4(g)+3 \mathrm{O}_2(g) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(l)+2 \mathrm{CO}_2(g) \Delta H_3^0=-1410 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{aligned}

## 物理代写|热力学代写Thermodynamics代考|First and Second Laws Combined

$50 \mathrm{~g}$ oxygen gas ( $298 \mathrm{~K}$ and $1 \mathrm{bar})$ expands reversibly and adiabatically to the double volume. Calculate the changes in internal energy $(\Delta U)$ and entropy $(\Delta S)$. Calculate also the entropy production $\left(\Delta S_{\mathrm{i}}\right)$. Assume that the gas follows the ideal gas law.

Make a calculation for the same gas ( $298 \mathrm{~K}$ and $1 \mathrm{bar})$. In this case, the gas expands into an evacuated container (Joule expansion). The volume of the gas is doubled by the expansion. Calculate $\Delta U, \Delta S$ and $\Delta S_{\mathrm{i}}$.

Water drops at $-15^{\circ} \mathrm{C}$ can exist for some time in a pure state. However, ultimately when touching ground, they freeze immediately making walking and driving a car a very dangerous activity. Show based on the second law that crystallization of liquid water at $-10^{\circ} \mathrm{C}$ is a spontaneous process. The following data are needed to solve the problem: $C_{\mathrm{p}, \mathrm{m}}$ (water) $=75.3 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}$, $C_{\mathrm{p}, \mathrm{m}}(\mathrm{ice})=37.7 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}, \Delta H_{\mathrm{m}, \mathrm{m}}=6024 \mathrm{~J} \mathrm{~mol}^{-1}$.

Show that the change in entropy $(\Delta S)$ of an ideal gas in $V-T$ space can be described by $\Delta S=C_{\mathrm{v}} \ln \left(T_2 / T_1\right)+n R \ln \left(V_2 / V_1\right)$.

Use the derived relationship together with other suitable equations to determine $\Delta \mathrm{S}$ for an ideal gas subjected to the following changes: (i) reversible isothermal expansion; (ii) reversible isochoric heating; (iii) isobaric change of state; (iv) reversible adiabatic expansion; and (v) free adiabatic expansion (Joule expansion).

Calculate the change in Gibbs free energy of melting of ice at normal pressure at the following temperatures: $-10{ }^{\circ} \mathrm{C}, 0{ }^{\circ} \mathrm{C}, 10^{\circ} \mathrm{C}$ and $30{ }^{\circ} \mathrm{C}$. The enthalpy of melting is $6024 \mathrm{~J} \mathrm{~mol}^{-1}$, and the entropy of melting is $22.05 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}$.

Derive the following relationships for the Gibbs free energy: $(\partial G / \partial T){p, n}=-S,(\partial G / \partial p){T, n}=V$ and $(\partial G / \partial n)_{T, p}=\mu$.

Show that the internal pressure $\left(\pi_{\mathrm{T}}\right)$ of an ideal gas is zero by applying one of the Maxwell relations on the combined first and second laws.

## 物理代写|热力学代写Thermodynamics代考|Thermodynamics Problems

$$\mathrm{H}2(g)+1 / 2 \mathrm{O}_2(g) \rightarrow \mathrm{H}_2 \mathrm{O}(l) \Delta H^0{ }_1=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \quad \mathrm{C}_2 \mathrm{H}_2(g)+2 \frac{1}{2} \mathrm{O}_2(g) \rightarrow \mathrm{H}_2 \mathrm{O}(l)+2 \mathrm{CO}_2(g) \Delta H_2^0=-1300 \mathrm{~kJ} \mathrm{~mol}^{-1} \mathrm{C}_2 \mathrm{H}_4(g)+3 \mathrm{O}_2(g) \rightarrow 2$$

## 物理代写|热力学代写Thermodynamics代考|First and Second Laws Combined

$C_{\mathrm{p}, \mathrm{m}}$ (ice $)=37.7 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}, \Delta H_{\mathrm{m}, \mathrm{m}}=6024 \mathrm{~J} \mathrm{~mol}^{-1}$.

$22.05 \mathrm{~J}(\mathrm{~K} \mathrm{~mol})^{-1}$

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