The temperature of a gas is $-50^{\circ}$C. To what temperature the gas should be heated so that the rms speed

Question

The temperature of a gas is $-50^{\circ}$C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?

Accepted Answer

$v_{rms} \propto \sqrt{T}$. If $v_{rms}$ increases by 3 times, final speed $v_f = 4v_i$. Thus $T_f = 4^2 T_i = 16 T_i$. Initial $T_i = -50 + 273 = 223$ K. $T_f = 16 	imes 223 = 3568$ K. In Celsius, $3568 - 273 = 3295^{\circ}$C.

Step-by-Step Solution

Practice All PHYSICS Questions