Ideal Gases and First Law of Thermodynamics

Ideal Gas Law

• $P$ is the pressure of the gas in $Pa$
• $V$ is the volume of the gas in $m^3$
• $n$ is the number of moles of the gas
• $R$ is the gas constant and is equal to $R=8.31446 \frac{J}{mol\cdot K}$
• $N$ is the number of atoms in the gas
• $k_B$ is the Boltzmann constant which is equal to:

• $k_B=\frac{R}{N_A}$ where $N_A$ is the Avogadro constant
• $N_A$ is the number of atoms in one mole of a given substance and is equal to $N_A=6.022\times10^{23} \frac{1}{mol}$

First Law of Thermodynamics

• Change in the internal thermal energy of the system is either due to heat exchange or work done on the gas or both:

• The internal thermal energy of an ideal gas is ONLY function of its temperature.

• $\Delta U>0$ if $\Delta T>0$ and $\Delta U<0$ if $∆T<0$
• $Q>0$ if the heat is added to the gas
• $Q<0$ if the heat is removed from the gas
• $W>0$ if the work is done by the gas
• $W<0$ if the work is done on the gas