Tag: kinetic theory of gases

Questions Related to kinetic theory of gases

The SI unit for the coefficient of cubical expansion is

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $^\circ C$

  2. $per^\circ C$

  3. $cm^{2}/^\circ C$

  4. none of these

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Correct Option: D
Explanation:
The SI unit of coefficient of cubical expansion is $K^{-1}$
$\gamma =\cfrac { 1 }{ V } \cfrac { dV }{ dT } =\cfrac { 1 }{ { metre }^{ 3 } } \cfrac { { metre }^{ 3 } }{ K } ={ K }^{ -1 }$

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\dfrac{1}{p}\dfrac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to.

physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. R

  2. $R^3$

  3. $\dfrac{1}{R}$

  4. $R^{2/3}$

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Correct Option: A
an ideal gas is expanding such that $PT^2$ $=costant$ The coefficient of volume expansion of the gas is__? 
physics kinetic theory of gases thermal expansion in gases thermal expansion of fluids volume elasticity constant of gases

  1. $1|T$

  2. $2|T$

  3. $3|T$

  4. $4|T$

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Correct Option: C

At what temperature volume of an ideal gas at $0^oC$  becomes triple by keeping pressure constant

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

  1. $546^oC$

  2. $182^oC$

  3. $819^oC$

  4. $646^oC$

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Correct Option: A

A container with insulating wall is divided into two equal parts by a partition fitted with a vaive.One part is filled with an ideal gas at pressure P and temperature T, whereas the other part is one part is  completely evacuated. If the valve is suddenly opened, the pressure and temperature of gas will be: 

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

  1. $P , \cfrac { T } { 2 }$

  2. $\cfrac { P } { 2 } , T$

  3. $\cfrac { P } { 2 } , \cfrac { T } { 2 }$

  4. $P , T$

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Correct Option: B

The number of air molecules in a $(5m\times5m\times4m)$ room at standard temperature and pressure is of the order of

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

  1. $6\times10^{23}$

  2. $3\times10^{24}$

  3. $3\times10^{27}$

  4. $6\times10^{30}$

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Correct Option: C

The relation PV=RT can describe the behavior of a real gas at :

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

  1. high temperature and high pressure

  2. high temperature and low pressure

  3. low temperature and low pressure

  4. low temperature and high pressure

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Correct Option: B
Explanation:

PV=RT is ideal gas equation and gases behave ideally only at high temperature and low pressure.
Therefore option(B).

A real gas behaves as an ideal gas :

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

  1. at very low pressure and high temperature

  2. high pressure and low temperature

  3. high temperature and high pressure

  4. low pressure and low temperature

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Correct Option: A
Explanation:
Real gas obeys vanderwaals equation 
$\left( p+\dfrac { n^{ 2 }a }{ V^{ 2 } }  \right) \left( V-nb \right) =nRT$
at high temperature and low pressure
Van der waal equation becomes approximately PV=nRT
Hence gases behave ideally at high temperature and low pressure.

The equation of state of a real gas can be expressed as $(P + \dfrac{a}{V _2}) (V - b) = cT$, where P is the pressure, V the volume, T the absolute temperature and a, b, c are constants. What are the dimensions of 'a'-

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

  1. $M^0 L^3 T^{-2}$

  2. $ M L^{-2} T^5$

  3. $M L^5 T{-2}$

  4. $M^0 L^3 T^0$

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Correct Option: C
Explanation:

$\left( {p + \frac{a}{{{V _2}}}} \right)\left( {v - b} \right) = cT$

$p$ is pressure, $V$ is volume and $T$ is temperature
$\begin{array}{l} p=\frac { F }{ A } =\frac { { ML{ T^{ -2 } } } }{ { { L^{ 2 } } } } =M{ L^{ -1 } }{ T^{ -2 } } \ V={ L^{ 3 } } \end{array}$
We cannot add or subtract quantities of different dimensions.
$\begin{array}{l} \therefore p=\frac { a }{ { { V^{ 2 } } } }  \ \Rightarrow a=\frac { p }{ { { V^{ 2 } } } } =\frac { { M{ L^{ -1 } }{ T^{ -2 } } } }{ { { { \left( { { L^{ 3 } } } \right)  }^{ 2 } } } } =M{ L^{ 5 } }{ T^{ -2 } } \end{array}$
Hence, Option $C$ is correct.

Diatomic gas at pressure `P' and volume `V' is compressed adiabatically to 1/32 times the original volume. Then
the final pressure is

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

  1. P/32

  2. 32 P

  3. 128 P

  4. P/128

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Correct Option: C