Question

Temperature of an ideal gas, initially at $27^{\circ}$C, is raised by $6^{\circ}$C. The rms velocity of the gas molecules will,

• A. increase by nearly 2%
• B. decrease by nearly 2%
• C. increase by nearly 1%
• D. decrease by nearly 1%

Answer 1

Answer: (C)

increase by nearly 1%

Answer 2

Initial temperature of ideal gas,
$T_{1}=273+27=300\, K$
when temperature of gas is raised by $6^{\circ} C$, the final temperature of gas
$T_{2} =273+6+27$
$=306\, K$
Let initial velocities are $v_{ rms _{1}}$, and $v_{ rms _{2}}$
$v_{ ms } \propto \sqrt{T}$
$\frac{v_{ rms _{1}}}{v_{ mms _{2}}} =\sqrt{\frac{T_{1}}{T_{2}}}$
$v_{ rms _{2}} =\sqrt{\frac{T_{2}}{T_{1}}} \times v_{ rm s_{1}}$
$=\sqrt{\frac{306}{300}} \times v_{ rms _{1}}$
$=1 \cdot 00 \times v_{ ms _{1}}$
So, it will increase by $1 \%$