Question

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is n. The internal energy of one mole of the gas is un and the speed of sound in the gas is vn. At a fixed temperature and pressure, which of the following is the correct option?

• A. v3 < v6 and 𝑈3 > 𝑈6
• B. v5 > v3 and 𝑈3 > 𝑈5
• C. v5 > v3 and 𝑈3 > 𝑈5
• D. v6 < v7 and 𝑈6 < 𝑈7

Answer 1

Answer: (C)

v5 > v3 and 𝑈3 > 𝑈5

Answer 2

$U_n=\frac{1\times n\times RT}{2}$
$=\frac{nRT}{2}$

$V_n=\sqrt{\frac{\gamma RT}{M}}$
$=\sqrt{\frac{(1+\frac{2}{n})RT}{M}}$

⇒$$U_7 > U_5\ \text{and}\ U_7 > U_6\ \text{ and}\ v_5 > v_7