Tag: kinetic theory of gases

Questions Related to kinetic theory of gases

The pressure cooker contains air at 1 atm and $ 3{0  }^{ 0 }C $ . If the safety value of the cooler blows when the inside pressure $ \ge 3 atm $ atm, the the maximum temperature of the air, inside the cooker can be 

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. $ 9{0 }^{ 0 }C $

  2. $ 63{6 }^{ 0 }C $

  3. $90{9 }^{ 0 }C $

  4. $ 36{3 }^{ 0 }C $

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Correct Option: A

The ratio of number of collisions per second at the walls of containers by $He$ and $O _2$ gas molecules kept at same volume and temperature, is (assume normal incidence on walls) ?

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. $2\sqrt{2} :1$

  2. $1:2$

  3. $2:1$

  4. $1:2\sqrt{2} $

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Correct Option: C

For a real gas, deviations from ideal gas behavior are maximum at 

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. $-10^o C$ and $5.0 \,atm$

  2. $-10^o C$ and $2.0 \,atm$

  3. $0^o C$ and $1.0 \,atm$

  4. $100^o C$ and $2.0 \,atm$

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Correct Option: A

As per Langmuir model of adsorption of a gas on a solid surface.

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. The mass of gas striking a surface area is independent of the pressure of the gas

  2. The adsorption can be multilayer.

  3. The rate of desorption does not depend on the pressure.

  4. The rate of desorption does not depend on the surface are adsorbed.

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Correct Option: C
Explanation:

In Langmuir's model of adsorption of a gas on solids surfaces. The adsorption at a single site on the surface may invoice multiple molecules at the ame time. The mass of gas striking at a given area of surface is independent of the pressure of the gas.

Under which of the following conditions is the law $pV=RT$ obeyed most closely by a real gas?

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. High pressure and high temperature.

  2. Low pressure and low temperature.

  3. High pressure and low temperature.

  4. Low pressure and high temperature.

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Correct Option: D
Explanation:

At low pressure and high temperature real gas obey PV=RT  i.e. they behave as ideal gas because at high temperature we can assume that there is no force of attraction or repulsion works among the molecules and the volume occupied by the molecules is negligible in comparison to the volume occupied by the gas

1 mole of $SO _2$ occupies a volume of $350 ml$ at $300K$ and $50 atm $ pressure. Calculate the compressibility factor of the gas.

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. $0.888$

  2. $0.711$

  3. $0.520$

  4. $0.987$

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Correct Option: B
Explanation:

Given $P=50 \ atm , \ \ V=350 ml =0.350 \ \ \ litre, \ \ n=1 \ \ mole $ and $ T=300 K$

Now, Compressibility factor $Z= \dfrac{PV}{nRT}$
$\therefore  \ Z= \dfrac{50 \times 0.350}{1 \times 0.082 \times 300}= 0.711$

A real gas behaves like an ideal gas if its.

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. Both pressure and temperature are high

  2. Both pressure and temperature are low

  3. Pressure is high and temperature is low

  4. Pressure is low and temperature is high

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Correct Option: D
Explanation:

At high temperature and low pressure the real gas behaves as an ideal gas.

The behaviour of the gases, which can be easily liquified, is like that of the

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. triatomic gases

  2. ideal gases

  3. van der Waals gases

  4. all of the above

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Correct Option: C
Explanation:

Van der Walls equation takes into account inter atomic forces between gas particles which is not considered in the ideal gas model. Since simplicity of  liquification of a gas depends upon forces between its particles, Van der Walls equation is followed by easily liquifieable gases. 


$(P+a(\dfrac { { n }^{ 2 } }{ { V }^{ 2 } } ))(V-nb)=nRT$

Parameter a takes into account interatomic forces.

The rms speed of the molecules of enclosed gas is V. What will be the ems speed if pressure is doubled, keeping the temperature same ?

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. 3 V

  2. 4 V

  3. V

  4. 2 V

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Correct Option: B

If 2g of helium is enclosed in a vessel at NTP, how much heat should be added to it to double the pressure ? (Specific heat of helium = 3 J/gm K)

real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

  1. 1638 J

  2. 1019 J

  3. 1568 J

  4. 836 J

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Correct Option: A
Explanation:

No. of moles, $n=\dfrac{m}{M}=\dfrac{2}{4}=0.5 mol$

The specific heat, $C _V=3J/g.mol K$
$C _V=12 J/mol. K$
At constant volume,
$\dfrac{T _2}{T _1}=\dfrac{P _1}{P _2}$
$T _2=2T _1$
$\Delta T=2T _1-T _1=T _1=273K$
The heat required, $\Delta Q=nC _V \Delta T$
$\Delta Q=0.5\times 12\times 273$
$\Delta Q=1638 J$
The correct option is A.