Question

a) Write the differential of pressure, dp, as a function of variables T,v (Temperature and Volume...

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

b) Write the differential of volume, dv, 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 dp by using the isothermal compressibility coefficient kr, and the coefficient of thermal expansion α.

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

kr - 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

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