Most Probable Speed

For a monotomic gas at temperature T, match the following columns. {:(,"ColumnI",, "ColumnII"),((A),"Speed of sound", (p),sqrt(2RT//M)),((B),"RMS speed of gas molecules",(q),sqrt(8RT//piM)),((C),"Average speed of gas molecules",(r),sqrt(3RT//M)),((D),"Most probable speed of gas molecules",(s),sqrt(5RT//3M)):}

Let barv,v_(rms) and v_p respectively denote the mean speed. Root mean square speed, and most probable speed of the molecules in an ideal monatomic gas at absolute temperature T. The mass of a molecule is m. Then

Consider the following statements and arrange in the order of true/false as given in the codes. S_1 :Speed possessed by maximum number of molecules of gas is called most probable speed S_2 :Molecular speeds are function of temperature for a particular gas. S_3 :If amount of gas is increased then most probable speed also increases. S_4 :The root mean square speed of an ideal gas is proportional to 1/sqrtd

Statement-1 :The area under the maxwell distribution molecular speed curve remains same irrespective of temperature of gas. Statement-2 :The fraction of molecules with most probable speed increases with increases of temperature.

A gas bulb of 1 L capacity contains 2.0xx10^(11) molecules of nitrogen exerting a pressure of 7.57xx10^(3)Nm^(-2) . Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square is 0.82 , calculate the most probable speed for these molecules at this temperature.

(a) Calculate the total and average kinetic energy of 32 g methane molecules at 27^(@)C (R=8.314 JK^(-1)mol^(-1)) (b) Also calculate the root mean square speed, average speed and most probable speed of methane molecules at 27^(@)C .