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# Gases-Theories, Laws Assignment Help

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Thermodynamics - Gases-Theories, Laws

**Gases-Theories, Laws**

Boyle’s law **p ∝ (1 / V) or PV **= constant

Charles’s law of pressure

**P ∝ V**^{2}rms or P ∝ T. V^{2} rms ∝ T

Avogadro’s law at the same temperature and pressure, equal volumes of all gases cons tin equal number of molecules.

Graham’ law of different when two gases at the same pressure and temperature are allowed to diffuse into each other, the rate of diffusion of each gas is inversely proportional to the square root of the density of the gas

**r**_{1} / r_{2} = √P_{2} / p_{1}

Diffusion coefficient **D = 1 / 3 A V average **

Dalton’s law of partial pressure the pressure exerted by a mixture of several gases equals the sum of the pressures exited by each gas occupying the same volume as that of the mixture.

**P = P**_{1} + P_{2} + …….

V average = √8KT / πm = √(8 RT) / π M

V most probable = √2KT /m = √2RT/ M

Maxwell’s speed distribution

**dN = 4 πN [ m / 2πKT]**^{3/2} v^{2} e ^{–mv2} / 2KT dv

Van der Waal’s equation of state

**[P + a / V**^{2}] (V – b) = RT (for one mole)

Or **[P + n**^{2} {a / V^{2}}] (V – nb) = n^{RT} for **n** moles

**V critical = B, P critical = a / 27b**^{2}.

T critical = 8a / 27 RB = 8 / 27 Tn

Where **T**_{n} is boyle’s temperature and **TB = a / RB**

**Relative humidity **

Vapour pressure of air = Saturated vapour pressure at the same temperature **OR** Saturated vapour pressure at dew point **OR **Saturated vapour pressure at air temperature

The amount of heat needed to raise the temperature of **1 g **of water by **1°C (14.5°C to 15.5°C) **at a pressure of **1 atm** is called a calorie.

Specific heat capacity **(c)** it is the amount of heat required to raise the temperature of a unit mass of substance by **1°C**

**C = ?Q / m ?θ [?θ----->** rise in temperature].

Latent heat it is the amount of heat required to change the state of unit mass of a substance from liquid to vapour or solid to liquid without changing the temperature. It in latent heat of vaporization** (liquid ---> vapour). **

Latent heat of fusion of ice (water) = **80 calg**^{-1}L = ?Q / M

Latent heat of vaporization of water =** 537 calg**^{-1}

Practically taken to be **540 calg**^{-1}.

Heat of sublimation amount of heat required to convert a solid (unit mass) directly to vapour (gas).

Hoar frost is reverse of sublimation. Freezing of clouds is an example.

Regulation is the melting of ice under pressure and its resolidification when pressure is removed. Variation of melting point in solids and baling point in liquid. **(TK)** is given by

**dp / dt = JL / TK (V final – V initial)**

Mechanical equivalent of heat,

**1 calorie = 4. 186 j (practically taken to be 4.2j)**

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**Gases-Theories, Laws**

**p ∝ (1 / V) or PV**= constant

Charles’s law of pressure

**P ∝ V**

^{2}rms or P ∝ T. V^{2}rms ∝ TAvogadro’s law at the same temperature and pressure, equal volumes of all gases cons tin equal number of molecules.

Graham’ law of different when two gases at the same pressure and temperature are allowed to diffuse into each other, the rate of diffusion of each gas is inversely proportional to the square root of the density of the gas

**r**

_{1}/ r_{2}= √P_{2}/ p_{1}

Diffusion coefficient

**D = 1 / 3 A V average**

Dalton’s law of partial pressure the pressure exerted by a mixture of several gases equals the sum of the pressures exited by each gas occupying the same volume as that of the mixture.

**P = P**

V average = √8KT / πm = √(8 RT) / π M

V most probable = √2KT /m = √2RT/ M

_{1}+ P_{2}+ …….V average = √8KT / πm = √(8 RT) / π M

V most probable = √2KT /m = √2RT/ M

Maxwell’s speed distribution

**dN = 4 πN [ m / 2πKT]**

^{3/2}v^{2}e^{–mv2}/ 2KT dvVan der Waal’s equation of state

**[P + a / V**(for one mole)

^{2}] (V – b) = RTOr

**[P + n**

^{2}{a / V^{2}}] (V – nb) = n^{RT}for

**n**moles

**V critical = B, P critical = a / 27b**

T critical = 8a / 27 RB = 8 / 27 Tn

^{2}.T critical = 8a / 27 RB = 8 / 27 Tn

Where

**T**

_{n}is boyle’s temperature and

**TB = a / RB**

**Relative humidity**

Vapour pressure of air = Saturated vapour pressure at the same temperature

**OR**Saturated vapour pressure at dew point

**OR**Saturated vapour pressure at air temperature

The amount of heat needed to raise the temperature of

**1 g**of water by

**1°C (14.5°C to 15.5°C)**at a pressure of

**1 atm**is called a calorie.

Specific heat capacity

**(c)**it is the amount of heat required to raise the temperature of a unit mass of substance by

**1°C**

**C = ?Q / m ?θ [?θ----->**rise in temperature].

Latent heat it is the amount of heat required to change the state of unit mass of a substance from liquid to vapour or solid to liquid without changing the temperature. It in latent heat of vaporization

**(liquid ---> vapour).**

Latent heat of fusion of ice (water) =

**80 calg**

^{-1}L = ?Q / MLatent heat of vaporization of water =

**537 calg**

^{-1}

Practically taken to be

**540 calg**

^{-1}.Heat of sublimation amount of heat required to convert a solid (unit mass) directly to vapour (gas).

Hoar frost is reverse of sublimation. Freezing of clouds is an example.

Regulation is the melting of ice under pressure and its resolidification when pressure is removed. Variation of melting point in solids and baling point in liquid.

**(TK)**is given by

**dp / dt = JL / TK (V final – V initial)**

Mechanical equivalent of heat,

**1 calorie = 4. 186 j (practically taken to be 4.2j)**

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