Kinetic Theory · Question 17

The molecules of a given mass of a gas have r.m.s. velocity of 200 m s-1 at 27 and 1.0 105 N m-2 pressure. When the temperature and pressure of the gas are respectively, 127 and 0.05 105 N m-2, the r.m.s. velocity of its molecules in m s-1 is

1. 100 23
2. 1003
3. 100 2
4. 400 3

A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas ?

1. P/(kT)
2. Pm/(kT)
3. P/(kTV)
4. mkT

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is

1. 2
2. 12
3. 23
4. 34

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K-1 mol-1. If the speed of sound in this gas at NTP is 952 m s-1, then the heat capacity at constant pressure is (Take gas constant R = 8.3 J K-1 mol-1)

1. 7.0 J K-1 mol-1
2. 8.5 J K-1 mol-1
3. 8.0 J K-1 mol-1
4. 7.5 J K-1 mol-1

The ratio of the specific heats CpCv = in terms of degrees of freedom (n) is given by

1. (1 + 2n )
2. (1 + n2 )
3. (1 + 1n )
4. (1 + n3 )

The mean free path of molecules of a gas, (radius r) is inversely proportional to

1. r3
2. r2
3. r
4. r

In the given (V - T) diagram, what is the relation between pressure P1 and P2? [figure]

1. P2 < P1
2. Cannot be predicted
3. P2 = P1
4. P2 > P1

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1 K to T2 K is

1. 34Na kB (T2 - T1)
2. 34Na kB ( T2T1 )
3. 38Na kB (T2 - T1)
4. 32Na kB (T2 - T1)

In a vessel, the gas is at pressure P. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

1. 2P
2. P
3. P/2
4. 4P

At 10 the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At 110 this ratio is

1. 10110x
2. 283383x
3. x
4. 383283x