The ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.
What is the RMS speed of an ideal gas?
The equation V = √((3RT)/M), where R is the universal gas constant, T is the absolute (Kelvin) temperature, and M is the molecular mass, gives the root mean square (R.M.S.) speed V of the molecules of an ideal gas.
How to solve the question?
In the question, we are asked to find the ratio of the RMS speed of an ideal gas at 235K and 37K.
We are given two temperatures, T₁ = 235K and T₂ = 37K
We calculate the ratio V₁:V₂ in the following way:
V₁:V₂
= √((3RT₁)/M)/√((3RT₂)/M)
= √((3R(235))/M)/√((3R(37))/M)
= √(235/37) {Since, 3, R, and M, cancel off each other}
= √6.351 = 2.52011.
Thus, the ratio of RMS speed of an ideal gas at 235K and 37K is 2.52011.
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