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Kinetic Theory Test - 65

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Kinetic Theory Test - 65
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  • Question 1
    1 / -0
    At what temperature will the rms speed of oxygen molecules become just sufficient for escaping form the Earth's atmosphere? (Given : mass of oxygen molecule $$\left( m \right) =2.76\times { 10 }^{ -26 }$$  kg, Boltzmann constant $$\left( { K }_{ B }=2.76\times { 10 }^{ -23 }{ JK }^{ -1 } \right) $$
    Solution
    At the minimum velocity with which the body must be projected vertically upwards so that it could escape from the earth's atmosphere is its escape velocity $$V_{e}$$
    As
    $$v_{l}=\sqrt{2gR}$$
    Substituting the value of g $$(9.8 ms^{-2})$$ and radius of earth $$(R=6.4\times 10^{6}m) $$ We get

    $$v_{e}=\sqrt{2\times9.8\times 64\times 10^{6}}$$

    $$\cong 11.2kms^{-1}=11200ms^{-1}$$
    Let the temperature of molecule be $$T$$ when it attains $$v_{e}$$.

    According to the question,

    $$v_{rms}=v_{e}$$
    where $$v_{rms}$$ is the $$rms$$ speed of the oxygen molecule,

    $$\Rightarrow \sqrt{\dfrac{3k_{B}T}{mo_{2}}}=11.2\times 10^{3}$$
    or $$T=\dfrac{(11.2\times 10^{3})^{2}(mo_{2})}{(3k_B)}$$

    Substituting the given values i.e 
    $$R_{B}=1.38\times 10^{-23} JK^{-1}$$ and 
    $$mo_2=m=2.76\times 10^{-26}kg$$

    We get,
    $$T=\dfrac{(11.2\times 10^{3})^{2}(2.76\times 10^{-26})}{(3\times 1.38\times 10^{-23})}$$

    $$=8.3626\times 10^{4}k$$
  • Question 2
    1 / -0
    One gram mole of helium at $$60C$$ is mixed with two gram moles of argon at $$30C$$ . The temperature of the mixture is 
    Solution

  • Question 3
    1 / -0
    Four litre of $${ CO }_{ 2 }$$ is kept at $$27^\circ C$$. What will be the volume if the temperature is lowered to 150 K at the same pressure.
  • Question 4
    1 / -0
    According to kinetic theory of gases kinetic energy of gas molecules:
  • Question 5
    1 / -0
    How much work to be done in decreasing the volume of an ideal gas by an amount of 2.4 x $$10^{-4} m^3$$ at constant normal pressure of 1 x $$10^5 N/m^2$$?
    Solution

  • Question 6
    1 / -0
    A flask breaks when pressure inside is 1.5 atmospheres. To what temperature can it be heated without breaking it if the initial pressure is atmospheric pressure at $$0C$$
  • Question 7
    1 / -0
    19 gms of oxygen occupies 5 liters at 2 at. when the pressure is increased to 2.8 at. and the volume is reduced to 4 lit the percentage increase of temperature is .
  • Question 8
    1 / -0
    One mole of gas occupies 10 ml at 50 mm pressure. The volume of 3 moles of the gas at 100 mm pressure and same temperature is 
    Solution

  • Question 9
    1 / -0
    The pressure of a given mass of gas is 100 cm at $${ 127 }^{ o }C$$ .The pressure of the same mass of gas having the same volume at $${ 27 }^{ o }C$$ is 
    Solution

  • Question 10
    1 / -0
    An open mounted bottle contains a gas at $${ 60 }^{ \circ  }$$C. What is the temperature to which the gas is to be heated so that 1/4 th mass of the gas may leave it.
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