Question

at constant pressure hydrogen is having temperature of 327 degree Celsius till what temperature it is to be cool so that the RMS velocity of its molecules become half of the earlier value

Answer 1

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Answer 2

Answer:

$T_{2}=150 K$

Explanation:

According to the kinetic theory of gas we know the relation between velocity and temperature of the gas.

$V_{rms} \alpha \sqrt{T}$..............................(1)

$T_{1}=600$

Since it is given that the RMS velocity of its molecules become half of the earlier value.

$V_{1rms}=V\\\\V_{2rms}=\dfrac{V}{2}$

We need to find $T_{1}=?$

Using equation (1) we get,

$\dfrac{V_{1rms} }{V_{2rms}}=\sqrt{\dfrac{T_{1}}{T_{2} } }$

$\dfrac{V }{\dfrac{V}{2}}=\sqrt{\dfrac{600}{T_{2} } }$

Squaring both sides we get,

$T_{2}=\dfrac{600}{4}\\\\T_{2}=150 K$