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Kinetic Theory Test - 70

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Kinetic Theory Test - 70
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  • Question 1
    1 / -0
    Find the approx. number of molecules contained in a Vessel of volume 7 litres at $$ 0^0 C\ at\ 1.3 \times 10^5 $$ pascal:
    Solution

  • Question 2
    1 / -0
    The quantity $$\dfrac{PV}{kT}$$ represents
    Solution
    The ideal gas equation is given as:
    $$PV=nRT$$

    The Boltzmann constant $$k$$ is represented as:
    $$k=\dfrac{R}{N}$$

    Now, substitute the value of the Boltzmann constant :
    $$PV=nkNT$$

    $$\therefore \dfrac{PV}{kT}=nN$$

    It is the number of molecules of the particular sample. SO, option $$D$$ is correct.
  • Question 3
    1 / -0
    Which of the following parameters is the same for molecules of all gases at a given temperature?
    Solution
    At a particular value of the temperature, the average kinetic energy of all the molecules is considered to be constant as temperature is the only factor that determines the kinetic energy of the molecules for the particular sample of gas.
    Thus, option $$D$$ is correct.
  • Question 4
    1 / -0
    Heat is added to an ideal gas and the gas expands. In such a process the temperature: 
    Solution

  • Question 5
    1 / -0
    A lead bullet just melts when stopped by an obstacle. Assuming that 25% of heat is absorbed by the obstacle, find the minimum velocity of the bullet if its initial temperature is $$27^{0}C$$ (melting point of lead $$327^{0}C$$; specific heat of lead $$= 0.03 \space cal/g^{0}C$$; latent heat of fusion of lead = 6 cal/g and J = 4.2 J/cal)
    Solution
    c. If mass of the bullet is m grams, heat absorbed by it to raise its temperature from $$27^{0}C$$ to $$327^{0}C$$ 
    $$mL = m \times 6 = 6 m\ cal$$

    So, the total heat required by the bullet
    $$ Q_1 = (9m + 6m) = 15 m cal = (15m \times 4.2) J$$
                                                            (as 1 cal = 4.2 J)
    Now when the bullet is stopped by the obstacle, loss in its mechanical energy.
    $$ME = \dfrac {1} {2} (m \times 10^{-3})v^{2} J$$     (as m gram =$$ m \times 10^{-3}$$ kg)

    As 25% of the energy is absorbed by the obstacle, the energy absorbed by the bullet
    $$Q_2 = \dfrac{75} {100} \times \dfrac {1} {2} mv^{2} \times 10^{-3} = \dfrac {3} {8} mv^{2} \times 10^{-3} J$$

    Now the bullet will melt if 
    $$ Q_2 \geq Q_1$$
    $$ \dfrac {3} {8} mv^{2} \times 10^{-3} \geq 15 m \times 4.2$$
    $$ v \geq \sqrt {(4 \times 4.2)} \times 10^{2}$$
    $$ v_{min} = 410 m/s$$
  • Question 6
    1 / -0
    Postulate of kinetic theory is
    Solution

    Postulates of Kinetic Theory of Gases :

    1) The molecules in a gas are small and very far apart. Most of the volume which a gas occupies is empty space.

    2) Gas molecules are in constant random motion. Just as many molecules are moving in one direction as in any other.

    3) Molecules can collide with each other and with the walls of the container. Collisions with the walls account for the pressure of the gas.

    4) When collisions occur, the molecules lose no kinetic energy; that is, the collisions are said to be perfectly elastic. The total kinetic energy of all the molecules remains constant unless there is some outside interference.

    5) The molecules exert no attractive or repulsive forces on one another except during the process of collision. Between collisions, they move in straight lines.

    Hence, Option "D" is the correct answer.

  • Question 7
    1 / -0
    The temperature of an ideal gas is kept constnat as it expands. The gas does external work. During this process, the internal energy of the gas
    Solution
    internal energy changes in an ideal gas may be described solely by changes in its kinetic energy. Kinetic energy is simply the internal energy of the perfect gas and Internal energy depends only on the temperature of the gas.
  • Question 8
    1 / -0
    Molecules of a gas behave like 
    Solution
    The molecules behave as rigid spheres. Pressure is due to collisions between the molecules and the walls of the container. All collisions, both between the molecules themselves, and between the molecules and the walls of the container, are perfectly elastic.
  • Question 9
    1 / -0
    Heat is not being exchanged in a body. If its internal energy is increased then
    Solution
    The internal energy depends on the temperature.
    If the internal energy will increase then the temperature will also increase.
  • Question 10
    1 / -0
    The internal energy of an ideal gas depends upon
    Solution
    The internal energy and enthalpy of ideal gases depends only on temperature, not on volume or pressure.
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