Question

5. For a van der Waal's gas, \begin{align} a) \text{ determine,} \left(\frac{\partial P}{\partial V}\right)_{T,N} \\ b) \text{ determine,} \left(\frac{\partial^2 P}{\partial V^2}\right)_{T,N} \\ c) \text{ Since the critical point is an inflection point on the phase diagram for a van der Waals} \\ \text{gas, both the first and second derivatives at that point are zero. Use this fact to determine} \\ \text{expressions for } P_c, V_c \text{ and } T_c \text{ that relate these critical values to a and b.} \\ d) \text{ Using the values, } a = 6.8 \times 10^{-50} J m^3 \text{ and } b = 4.4 \times 10^{-29} m^3, \text{ determine the critical} \\ \text{pressure, temperature and volume for one mole of hydrogen gas.} \end{align}

          5.
For a van der Waal's gas,
\begin{align*}
a) \text{ determine,} \left(\frac{\partial P}{\partial V}\right)_{T,N} \\
b) \text{ determine,} \left(\frac{\partial^2 P}{\partial V^2}\right)_{T,N} \\
c) \text{ Since the critical point is an inflection point on the phase diagram for a van der Waals} \\
\text{gas, both the first and second derivatives at that point are zero. Use this fact to determine} \\
\text{expressions for } P_c, V_c \text{ and } T_c \text{ that relate these critical values to a and b.} \\
d) \text{ Using the values, } a = 6.8 \times 10^{-50} J m^3 \text{ and } b = 4.4 \times 10^{-29} m^3, \text{ determine the critical} \\
\text{pressure, temperature and volume for one mole of hydrogen gas.}
\end{align*}

5.
For a van der Waal's gas,

a) determine,((∂ P)/(∂ V))T,N

b) determine,((∂^2 P)/(∂ V^2))T,N

c) Since the critical point is an inflection point on the phase diagram for a van der Waals
gas, both the first and second derivatives at that point are zero. Use this fact to determine
expressions for Pc, Vc and Tc that relate these critical values to a and b.

d) Using the values, a = 6.8 × 10^-50 J m^3 and b = 4.4 × 10^-29 m^3, determine the critical
pressure, temperature and volume for one mole of hydrogen gas.

Added by Juan Francisco M.

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