Ideal Gas $($Work and Energy$)$:

Learning objectives:

Calculate energy and enthalpy changes during a process using a detailed heat capacity fit.

Understand relationship between $$ and molecular structure.

A closed rigid vessel contains $5$ kg of an ideal gas with a molecular weight of

$\frac{?}{\text{b}\text{a}\text{r}}(m)=18\mathrm{.}0k\frac{g}{k}$mol. The specific heat at constant pressure, $c_p,$ of the gas is given in NIST

polynomial form as

$\frac{?}{\text{b}\text{a}\text{r}}(c{)}_p=A+B+C{}^2+D{}^3+\frac{E}{{}^2}$

where $=\frac{T}{1000}K,T$ is in Kelvin, and $\frac{?}{\text{b}\text{a}\text{r}}(c{)}_p$ is in $\frac{J}{m}$olK. The coefficients over the range

$500T1700K$ are given below.

The gas is initially at a pressure of $3\mathrm{.}0$ atm and a temperature of $1250$ K $.$ The gas pressure is

then reduced to $1\mathrm{.}0$ atm without changing the density of the gas.

$($a$)$ Find the changes in internal energy, $E,$ and enthalpy, $H,$ of the gas in kJ during this

process and the amount of work done to the gas.

$($b$)$ Include a sketch of the process on a $p-v$ diagram. How can you graphically confirm the

amount of work done in part $($a$)?$

$($c$)$ What is the specific heat ratio, $,$ for this gas at $500$ K $.$ Explain whether you think it is a

diatomic gas or not.