NEET
Practice Test 6
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The gases are at absolute temperature 300°K and 350°K respectively. The ratio of average kinetic energy of their molecules is

If one mole of a monatomic gas(γ = 5/3) is mixed with one mole of a diatomic gas (γ = 7/3), the value of g for the mixture is

  • Solution

    Let γ1 and γ2 denote the ratio of two specific heats of gas 1 and gas 2 respectively when they are mixed in the ratio of n1 and n2 mole. The resultant value of γ is the weighted mean of γ1 and γ2 i.e.,

    \(\gamma =\frac{n_{1}\gamma _{1}+n_{2}\gamma _{2}}{n_{1}+n_{2}}=\frac{1(5 / 3)+1(7 / 5)}{1+1}\)

    \(=\frac{25+21}{15\times 2}=\frac{46}{30}=1.53\)

A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean square velocity of its molecules is doubled. The new volume will be

  • Solution

    Since Vrms is doubled by increasing the temp. so by

    \(V_{rms}=\sqrt{\frac{3KT}{m}}\), the temp. increase by four times.

    Now for constant pressure \(\frac{V_{1}}{T_{1}}\)

    V1 = V, T1 = T°K, T2 = 4T°K, V2 = ?.

    V2 = 4V

The r.m.s. velocity of oxygen molecule at 16 °C is 474 m/sec. The r.m.s. velocity in m/s of hydrogen molecule at 127 °C is

  • Solution

    \(V_{oxg}=\sqrt{\frac{3R\times 289}{32}}\: \: \: \: \: \left ( V_{rms}=\sqrt{\frac{3RT}{M}} \right )\)

    \(V_{H}=\sqrt{\frac{3R\times 400}{2}}\)

    So VH = 2230.59 m/sec

DIRECTIONS: Each of these question contains two statements: STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Answer these questions from the following four options.

Statement 1 : Mean free path of a gas molecules varies inversely as density of the gas.

Statement 2 : Mean free path varies inversely as pressure of the gas.

  • Solution

    (a)Statement-1 is True, Statement-2 is True;Statement-2 is a correct explanation for Statement -1

DIRECTIONS: Each of these question contains two statements: STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Answer these questions from the following four options.

Statement 1 : The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.
Statement 2 : The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

  • Solution

    (b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1

    Total translational kinetic energy =3⁄2nRT=3⁄2PV In an ideal gas all molecules moving randomly in all direction collide and their velocity changes after collision

DIRECTIONS: Each of these question contains two statements: STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Answer these questions from the following four options.

Statement 1 : Air pressure in a car tyre increases during driving.

Statement 2 : Absolute zero temperature is not zero energy temperature.

  • Solution

    (b)Statement-1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement - 1

    When a person is driving a car then the temperature of air inside the tyre is increased because of motion.From the Gay Lussac’s law,

    P α T

    Hence, when temperature increases the pressure also increase.

DIRECTIONS: Each of these question contains two statements: STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). Answer these questions from the following four options.

Statement 1 : The ratio CV⁄CP for a monatomic gas is less than for a diatomic gas.

Statement 2 : The molecules of a monatomic gas have more degrees of freedom than those of a diatomic gas.

  • Solution

    (c)Statement-1 is True, Statement- 2 is False

If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K, when no work is done, is

  • Solution

P,V,T respectively denote pressure, volume and temperature of two gases. On mixing, new temperature and volume are respectively T and V. Final pressure of the mixture is

  • Solution

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KINETIC THEORY OF GASES
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