Q: The temperature of an ideal gas is increased from 120 ~K to 480 ~K . If at 120 ~K , the root mean square velocity of the gas molecules is v, at 480 ~K it becomes

$ v _ 1 v _ 2 = 3 RT _ 1 M 3 RT _ 2 M = T _ 1 ~T _ 2 v _ 2 =2 v _ 1 $

Question 1

In a mixture of gases, the average number of degree of freedoms per molecule is 6 . The rms speed of the molecule of the gas is c, then the velocity of sound in the gas is

Accepted Answer

(v_ rms = 3 R T M and v_ sound = R T M v_ sound v_ rms = 3 Degree of freedom is 6 . array lr & =1+ 2 f =1+ 2 6 = 4 3 \ & v_ sound = 4 / 3 3 v_ rms = 2 3 v_ rms = 2 c 3 array

Question 2

The temperature of an ideal gas is increased from 200 K to 800 K . If r.m.s. speed of gas at 200 K is v_0. Then, r.m.s. speed of the gas at 800 K will be:

Accepted Answer

RMS speed, V _ rms = 3 RT M V _ mm T Here, T _ initiol =200 ~K T _ fing1 =800 ~K Initial RMS speed = v _0 v_0 v_ rms = 200 800 v_ ms =2 v_0

Question 3

Two vessels A and B are of the same size and are at same temperature. A contains 1 g of hydrogen and B contains 1 g of oxygen. P _ A and P_B are the pressures of the gases in A and B respectively, the

Accepted Answer

n _ A = 1 2 ~mol , n _ B = 1 32 ~mol By ideal gas equation, P V=n R T P n P _ A P _ B = n _ A n _ B = 32 2 =16

Question 4

A flask contains hydrogen and oxygen in the ratio of 2: 1 by mass at temperature 27^ C . The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

Accepted Answer

Average kinetic energy for diatomic gases aligned & K _ av = 5 2 kT \ & ( K _ av )_ H ( K _ av )_ O = (27+273) (27+273) =1 aligned

Question 5

A bicycle tyre is filled with air having pressure of 270 kPa at 27^ C . The approximate pressure of the air in the tyre when the temperature increases to 36^ C is

Accepted Answer

From the ideal gas equation PV = nRT Here, volume is constant P _1 ~T _1 = P _2 ~T _2 Here, T_1=27+273=300 ~K P_1=270 kPa T _2=36+273=309 ~K P_2= P_1 T_1 T_2= 270 (309) 300 =278 kPa

Question 6

A monoatomic gas of molar mass m is kept in a insulated container. Container is moving with velocity v. If the container is suddenly stopped, then the change in the temperature of the gas is

Accepted Answer

Let the insulated container has n moles of the monoatomic gas. The loss of kinetic energy of the gas, E_K= 1 2 (m n) v^2 If the change in temperature of the gas is T, then heat gained by the gas is, Q= 3 2 n R T Now, according to question, aligned Q & = E_K \ 3 2 n R T & = 1 2 m n v^2 \ T & = m v^2 3 R aligned

Question 7

One mole of an ideal diatomic gas undergoes a process as shown in the figure. The molar specific heat of the gas in the process is

Accepted Answer

In the curve, V 1 T aligned & V=m 1 T where, m= slope of curve. \ & V T= constant \ & T d V+V d T=0 \ & d V=- V T d T \ & As, Q= U+W \ & C d T=C_V d T+p d V \ & C d T=C_V d T- p T V d T \ & C=C_V- p V T \ & =C_V-R ( p V T =R ) \ & aligned For diatomic gas, C_V= 5 2 R C=C_V-R= 5 2 R-R= 3 R 2

Question 8

The temperature of an ideal gas is increased from 120 ~K to 480 ~K . If at 120 ~K , the root mean square velocity of the gas molecules is v, at 480 ~K it becomes

Accepted Answer

$ v _ 1 v _ 2 = 3 RT _ 1 M 3 RT _ 2 M = T _ 1 ~T _ 2 v _ 2 =2 v _ 1 $

Kinetic Theory of Gases — Previous Year Questions & Solutions