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

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

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

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

  1. $546^oC$

  2. $182^oC$

  3. $819^oC$

  4. $646^oC$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using Charles's Law (V1/T1 = V2/T2) at constant pressure, if V2 = 3*V1, then T2 = 3*T1. Given T1 = 0 C = 273 K, T2 = 3 * 273 = 819 K. Converting back to Celsius, 819 - 273 = 546 C.

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

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: 

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

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

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

  4. $P , T$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a free expansion (Joule expansion) into a vacuum. Since the walls are insulating (adiabatic) and no work is done (expansion against vacuum), the internal energy remains constant, meaning temperature T remains constant. The volume doubles, so by PV = nRT, the pressure must halve to P/2.

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

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

  1. $6\times10^{23}$

  2. $3\times10^{24}$

  3. $3\times10^{27}$

  4. $6\times10^{30}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = 5*5*4 = 100 m^3. At STP, 1 mole occupies 22.4 liters (0.0224 m^3). Number of moles n = 100 / 0.0224 approx 4464 moles. Number of molecules = n * Avogadro's number = 4464 * 6e23 approx 2.68e27, which is of the order of 10^27.

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

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

  1. high temperature and high pressure

  2. high temperature and low pressure

  3. low temperature and low pressure

  4. low temperature and high pressure
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

A real gas behaves as an ideal gas :

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.
Multiple choice real gases van der-waal equation: equation of state for real gas kinetic theory of gases thermal physics physics

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'-

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

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

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

  4. $M^0 L^3 T^0$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. P/32

  2. 32 P

  3. 128 P

  4. P/128
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For adiabatic processes, P * V^gamma = constant. For a diatomic gas, gamma = 1.4 or 7/5. P2 = P1 * (V1/V2)^gamma. Here V1/V2 = 32. P2 = P * (32)^(7/5) = P * (2^5)^(7/5) = P * 2^7 = 128P.

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

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) ?

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

  2. $1:2$

  3. $2:1$

  4. $1:2\sqrt{2} $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The rate of collisions per unit area is proportional to (n * v_avg), where n is number density and v_avg is average speed. Since n = N/V and V, T are same, n is same. v_avg is proportional to 1/sqrt(M). Ratio = v_He / v_O2 = sqrt(M_O2 / M_He) = sqrt(32 / 4) = sqrt(8) = 2*sqrt(2).

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

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

  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 $2.0 \,atm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Real gases deviate most from ideal behavior at high pressures and low temperatures, where intermolecular forces and molecular volume become significant.