Tag: van der-waal equation: equation of state for real gas

Questions Related to van der-waal equation: equation of state for real gas

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

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