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For Boyle's law to hold the gas should be :

Perfect and of constant mass and temperature

Real and of constant mass and temperature

Perfect and at a constant temperature but variable mass

Real and at a constant temperature but variable mass

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Explanation

1. Boyle’s law states that at constant temperature, pressure of given mass of a gas is inversely

proportional to its volume. This law is applicable for perfect gas only.

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Consider a 1 c.c. sample of air at the absolute temperature $T_{0}$ at sea level and another 1 c.c. sample of air at a height where the pressure is the one-third atmosphere. The absolute temperature T of the sample at that height is :

Equal to $T_{0} / 3$

Equal to $3 / T_{0}$

Equal to $T_{0}$

Cannot be determined in terms of $T_{0}$ from the above data

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Explanation

Mass of 1 cc of gas at sea level and at a given height does not remain the same and gas laws hold only for a constant.

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To double the volume of a given mass of an ideal gas at 27°C keeping the pressure constant, one must raise the temperature in degree centigrade to

54°

270°

327°

600°

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Explanation

$V \propto T \Rightarrow \frac{V_{1}}{V_{2}} = \frac{T_{1}}{T_{2}} \Rightarrow \frac{V}{2 V} = \frac{(273 + 27)}{T_{2}} = \frac{300}{T_{2}} \Rightarrow T_{2} = 600 K = 327 ° C$

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Which of the following statements about kinetic theory of gases is wrong

The molecules of a gas are in continuous random motion

The molecules continuously undergo inelastic collisions

The molecules do not interact with each other except during collisions

The collisions amongst the molecules are of short duration

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Explanation

2. The collision of molecules of ideal gas is elastic collision.

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If a Vander-Waal's gas expands freely, then final temperature is

Less than the initial temperature

Equal to the initial temperature

More than the initial temperature

Less or more than the initial temperature depending on the nature of the gas

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Explanation

1. In free expansion of Vander waal’s gas, its temperature decreases.

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In Vander Waal's equation $[P + \frac{a}{V^{2}}] (V - b) = RT,$ the dimensions of a are

$M^{1} L^{5} T^{- 2}$

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

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

$M^{1} L^{1} T^{- 2}$

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Explanation

1. According to the principle of homogeneity dimensional of $P$ = Dimension of $\frac{a}{V^{2}}$

$\Rightarrow \frac{a}{{[L^{3}]}^{2}} = [{ML}^{- 1} T^{- 1}] \Rightarrow a = [{ML}^{5} T^{- 2}]$

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Which law states that effect of pressure is same for all portion

Pascal’s law

Gay-lussac’s law

Dalton’s law

None of these

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Explanation

1. Pascal’s law

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The equation for an ideal gas is PV = RT, where V represents the volume of

1 gm gas

Any mass of the gas

One gm mol gas

One litre gas

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Explanation

3. The given equation is for 1 gm mol gas.

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

High pressure and high temperature

Low pressure and low temperature

Low pressure and high temperature

High pressure and low temperature

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Explanation

3. At low pressure and high temperature real gases behaves like ideal gases.

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The gas equation $\frac{PV}{T} =$ constant is true for a constant mass of an ideal gas undergoing

Isothermal change

Adiabatic change

Isobaric change

Any type of change

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Explanation

4. Any type of change

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