Answer to Question #100835 in Electric Circuits for Rishitha

Question

A gas mixture consists of 2moles of oxygen and 4 moles of argon at temperature T.Neglecting all vibrational mode,the total internal energy of the system is

Answer 1

Formula for the calculation of internal energy is $U=nC_vT$

where n is the number of moles, $T$ is the temperature and $C_v$ is the molar specific heat capacity

$C_v$ is given by $fR/2$ where $f$ is the degree of freedom

in case of oxygen, $f=5$ as oxygen is a diatomic gas

in case of argon, $f=3$ as argon is a mono-atomic gas

hence, $C_v=$ $5R/2$ for oxygen and $C_v=3R/2$ for argon

$U_{total}=U_{oxygen}+U_{argon}$

$U_{total}=2*(5R/2)*T + 4*(3R/2)*T$

$U_{total}=5RT+6RT$

$U_{total}=11RT$