Question

a) Write the differential of pressure, d*p*, as a
function of variables *T*,v (Temperature and Volume
respectively)

b) Write the differential of volume, d*v*, as a function
of variables *T*,p (Temperature and Pressure
respectively)

c) Write out a mathematical expression for d ln(v) (the
differential of the natural logarithm of volume) and an expression
for d*p* by using the isothermal compressibility coefficient
k_{r}, and the coefficient of thermal expansion α.

d) use the chain rule, and prove that a Van Der Waals Gas
satisfies R · k_{r} = α · (v - b)

k_{r} - the isothermal compressibility coefficient

α - the coefficient of thermal expansion

b - coefficient in the Van Der Waals equation

v - the molar volume of the gas

R - the gas constant

Answer #1

The van der Waals equation of state is (P + a(n/V )^2)(V/n − b)
= RT, where a and b are gas-specific constants. For Hydrogen gas, a
= 2.45 × 10^-2P a · m^6 and b = 26.61 × 10^-6m^3/mol, while for an
ideal gas a = b = 0. (a) Consider trying to measure the ideal gas
constant in a lab from the relation R = P V/(nT), where P, V, n,
and T are all measured parameters. However,...

At a constant temperature, the number of moles (n) of an ideal
gas is a function of two variables ? = ?(?, ?) where P is the
pressure and V is the volume (Remember the ideal gas law ?? = ???,
where R is the universal gas constant). The number of moles
function is given as ? = ?(?, ?) = −? 2 + 4? − ? 2 + 6?. Find the
maximum and minimum values of the number of...

1 mole of a gas undergoes a mechanically reversible isothermal
expansion from an initial volume 1 liter to a final volume 10 liter
at 25oC. In the process, 2.3 kJ of heat is absorbed in the system
from the surrounding. The gas follows the following formula:
V=RTP+b where V is the molar specific volume, and Tand Pare
temperature (abosolute) and gas pressure respectively. Given R=
8.314 J/(mol.K) and b= 0.0005 m3. Evaluate the following a) Work
(include sign) b) Change...

The ideal gas law
PV=nRT
relates pressure P, volume V, temperature
T, and number of moles of a gas, n. The gas
constant Requals 0.08206 L⋅atm/(K⋅mol) or 8.3145
J/(K⋅mol). The equation can be rearranged as follows to solve for
n:
n=PVRT
This equation is useful when dealing with gaseous reactions
because stoichiometric calculations involve mole ratios.
A)When heated, calcium carbonate decomposes to yield calcium
oxide and carbon dioxide gas via the reaction
CaCO3(s)→CaO(s)+CO2(g)
What is the mass of calcium carbonate...

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