Question

The degree of freedom of an ideal gas is n. The internal energy of 1 mole of the gas is Un and the speed of sound n the gas is Vn. At a fixed temperature and pressure, which of the following is correct?

• A. V5>V7 and U5>U7
• B. V5>V3 and U3>U5
• C. V3U6
• D. V6>V7 and U6<U7

Answer 1

Answer: (D)

V6>V7 and U6<U7

Answer 2

The correct option is (D): V6>V7 and U6<U7.
$V=\sqrt{\frac{\gamma RT}{M_0}}\,\, where\,\gamma =1+\frac{2}{n}$
and $U=n'\frac{n}{2RT}$
If n is more, $\gamma$ will be less, so $V_{sound}$ will also be less, but the internal energy U will be more.