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The ratio of the specific heats CP/CV=γ in terms of degrees of freedom (n) is given by -

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Explanation

(c)

The specific heat of the gas at constant volume in terms of the degrees of freedom n is -

CV=n2R

Also CP-CV=R

So, CP=n2R+R=R(1+n2)

Now, γ=CP/CV=R(1+n2)/n/2R=2n+1

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:

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A monoatomic gas at a pressure p, having a volume V expands isothermally to a volume 2 V and then adiabatically to a volume 16 V. The final pressure of the gas is: (take  γ=5/3)

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Explanation

(c)

For isothermal expansion 

ρV=ρ' x 2V [∴ V=2V]

ρ'=ρ/2

For adiabatic expansion,

PVγ=const.Here γ=53 P'(2V)53=Pf(16V)53Pf=P221653=P64                    P'=P2

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

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Explanation

Mean free path l=1/nπr2 

l ∝ 1/r2

The molar specific heats of an ideal gas at constant pressure and volume are denoted by CP and CV respectively. If γ=CP/CV and R is the universal gas constant, then CV is equal to

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Explanation

(b) The value of CV=R/γ-1

If Cp and Cv denote the specific heats (per unit mass) of an ideal gas of molecular weight M

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Explanation

             Cp-Cv=R  MCp-MCv=R              Cp-Cv=RM

Two gases of equal mass are in thermal equilibrium. If Pa, Pb and Va and Vb are their respective pressures and volumes, then which relation is true

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Explanation

4. Thermal equilibrium implies that the temperature of gases is the same. Hence Boyle’s law is

    applicable i.e.       PaVa = PbVb

The vapor of a substance behaves as a gas :

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Explanation

2. The vecotor of a substance behaves  as a gas above critical temperature as it can not be cooled down by pressure.

The temperature below which gas should be cooled, before it can be liquified by pressure only is termed as :

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Explanation

4. Critical temperature is the temperature below which a gas can be cooled by pressure only.

The mean free path of gas molecules depends on (d = molecular diameter)

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Explanation

3. Mean free path λ=12πd2n  λd-2

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