Flue gases rise through the cylindrical pipe. At the bottom of the pipe, they have a temperature of 700⁰C

Flue gases rise through the cylindrical pipe. At the bottom of the pipe, they have a temperature of 700⁰C and move at a speed of 5 m / s. At what speed do they move at the top of the pipe, where their temperature is 200 ° C?

The root-mean-square velocity of molecules in a gas is determined by the formula:

v = √ (2RT / M), where R is the universal gas constant, T is temperature, M is molar mass. We write this equation for the gas at the bottom of the pipe:

v0 = √ (2R * T0 / M).

Let us express the molar mass from it:

v0 ^ 2 = 2RT / M;

M = 2RT / v0 ^ 2.

The equation for the velocity at the top of the pipe will look similar:

v = √2RT1 / M, T1 is the temperature at the top.

Substituting the formula for M into it, we get:

v = √T1 / T0 * v0.

v = √200 / 700 * 5 = 1.2 m / s.

Answer: the required speed is 1.2 m / s.