\"As long as it doesn\'t kill you, college is a lot of fun.\" -L According to th

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"As long as it doesn't kill you, college is a lot of fun." -L According to the ideal gas law pV - nRT Starting with eq 1.1, find the following two partial derivatives: (partial differential V/partial differential T)_n, p and (partial differential V/partial differential p)_n, T The isothermal compressibility of a substance, kappa _T, is defined by the equation kappa _T = (1/V) (partial differential V/partial differential T)_n, p kappa_T is a measure of the relative change in volume that occurs when a substance is heated under conditions of constant pressure. Starting from eq 1.2, show that kappa_T is also given by the expression kappa _T = (1/V_m) (partial differential V_m/partial differential T)_n, p where V_m = V/n, the molar volume of the substance. Find the value for kappa_T for an ideal gas. Simplify your final expression as much The molar volume occupied by a solid is ten represented by the empirical expression V_m = V_0 + aT + bp + cpT where V_o, a, b, and c are constants whose values are found by fitting eq 1.4 to experimental data. Find the value of kappa_T for a substance whose molar volume is given by 1.4. Simplify your final expression its much as possible. Consider 1.000 mol of nitrogen gas (N_2) at an initial temperature T = 300.0 K and an initial pressure p = 1.000 bar. the can be assumed ideal, and the constant pressure molar heat capacity of the gas, C_p, m is given by the expression.

Explanation / Answer

part-c:

from equation 1.2,

kT = 1/V (dV/dT)

given Vm = V/n

So,

kT = 1/nVm ( d nVm /dT )

= n/n 1/Vm ( dVm/dT)

= 1/Vm ( dVm/dT)

For ideal gas , PVm = RT

dVm/dT = R/P and 1/Vm = P/RT

So,

kT = P/RT x R/P

= 1/T

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