Heat and Thermodynamics 4 Question 11

13. A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature $T$. Considering only translational and rotational modes, the total internal energy of the system is

(2019 Main, 11 Jan I)

(a) $12 R T$

(b) $15 R T$

(c) $20 R T$

(d) $4 R T$

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Answer:

Correct Answer: 13. (b)

Solution:

  1. Internal energy of a gas with $f$ degree of freedom is

$U=\frac{n f R T}{2}$, where $n$ is the number of moles.

Internal energy due to $O _2$ gas which is a diatomic gas is

$U _1=\frac{n _1 f _1 R T}{2}=3 \times \frac{5}{2} R T$

$\left(\because n _1=3\right.$ moles, degree of freedom for a diatomic gas $f _1=5$ )

Internal energy due to Ar gas which is a monoatomic gas is

$$ U _2=\frac{n _2 f _2 R T}{2}=5 \times \frac{3}{2} R T $$

$\left(\because n _2=5\right.$ moles, degree of freedom for a monoatomic gas $f _2=3$ )

$\therefore$ Total internal energy $=U _1+U _2$

$$ \Rightarrow \quad U=15 R T $$



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