Heat and Thermodynamics 4 Question 21

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

(1999, 2M)

(a) $4 R T$

(b) $15 R T$

(c) $9 R T$

(d) $11 R T$

Show Answer

Answer:

Correct Answer: 23. (d)

Solution:

  1. Internal energy of $n$ moles of an ideal gas at temperature $T$ is given by

$$ U=n\left(\frac{f}{2} R T\right) $$

where, $\quad f=$ degrees of freedom.

$$ =5 \text { for } O _2 \text { and } 3 \text { for } Ar $$

Hence, $\quad U=U _{O _2}+U _{Ar}=2\left(\frac{5}{2} R T\right)+4\left(\frac{3}{2} R T\right)=11 R T$



NCERT Chapter Video Solution

Dual Pane