Question

An ideal monoatomic gas is kept in a rigid container that expands negligibly when heated. The gas starts at a temperature of 17.0 deg C, and heat is added to increase its temperature. At what temperature will its root-mean-square speed (thermal speed) be 1.2 times its value at 17.0 deg C (20 % increase)

Answer 1

145 ° C

Step-by-step explanation:

Using the expression

`V_(rms) = \sqrt{(3RT)/(M) }`

where T = 17 ° C = (273 + 17) K

= 290 K

`V_(rms) = 1.2`

So; At what temperature will its root-mean-square speed (thermal speed) be 1.2 times its value at 17.0 deg C?

What this implies is that:

`\sqrt{(3RT)/(M) }= 1.2 \sqrt{(3*R*290)/(M) }` where R & M are constant

T = 144.6 ° C

T = 145 ° C