Question

When the temperature of an ideal gas is increased by 600 K, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is:

• A. $-73{}^{\circ }C$
• B. $27{}^{\circ }C$
• C. $127{}^{\circ }C$
• D. $327{}^{\circ }C$

Answer 1

Answer: (B)

Let initial temperature is T ie $T_1=T$ Then, $T_2=T+600$ Velocity of sound in gas $v\propto \sqrt{T}$ $\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}$ According to questions $v_2=\sqrt{3}{v}_1$ $\frac{\sqrt{3}{v}_1}{v_1}=\sqrt{\frac{T+600}{T}}$ $\sqrt{3}=\sqrt{\frac{T+600}{T}}$ $\therefore$ $3T=T+600$ $T=300K$ $=300-273=27{}^{o}C$