Complete Question
Argon gas (a monatomic gas) is sometimes used to insulate a double-pane window for purposes of insulation. In a particular window, the space in between two glass sheets has a volume of [tex]0.025 \ m^3[/tex]. If the temperature of the gas is 290 K. what is the rms speed of the gas atoms? The atomic mass of Argon is 39.9 u.(l u= 1.66x10-27 kg) Enter your answer in m/s
Answer:
The value is [tex]V_{rms} = 425.75 \ m/s[/tex]
Explanation:
From the question we are told that
The volume of the space in between the two glass sheet is [tex]a = 0.025 \ m^3[/tex]
The temperature of the gas is [tex]T = 290 \ K[/tex]
The atomic mass of Argon is [tex]m = 39.9 \ u = 39.9 * 1.66 *10^{-27} = 6.623 *10^{-26} \ kg[/tex]
Generally the root mean square velocity is mathematically represented as
[tex]V_{rms} = \sqrt{\frac{3 K T}{ m } }[/tex]
Here K is the Boltzmann constant with value [tex]k = 1.38 *10^{-23} \ m^3 \cdot kg \cdot s^{-2} \cdot K^{-1}[/tex]
So
[tex]V_{rms} = \sqrt{\frac{3 * 1.38 *10^{-23} * 290 }{ 6.6234*10^{-26} } }[/tex]
=> [tex]V_{rms} = 425.75 \ m/s[/tex]
