The rootmeansquare speed thermal speed for a certain gas at

The root-mean-square speed (thermal speed) for a certain gas at 100 degree C is 0.500 km/s. If the temperature of the gas is now increased to 200 degree C, the root-mean-square(thermal) speed will be closest to 563 m/s. 1000 m/s 634m/s 707 m/s 804 m/s

Solution

The root mean square of a gas is given as Vrms = Sqrt (3RT/M) where T is the temperature in Kelvin

Now, as for the given situation, the temperature is being changed from 100 degree celsius or 373.15 kelvin to 200 degree celsius or 473.15 kelvin

That is, Vrms = 0.5 = sqrt(3R373.15 / M)

Vrms(new) = sqrt(3R473.15 /M)

We divide the both equations to get:

Vrms (new) / 0.5 = sqrt(473.15 / 373.15)

Therefore, Vrms(new) = 0.563 km/s