# Charles’s law , Jolly’s law and General gas law

**The gases contract by cooling and expand by heating , Equal volumes of different gases expand equally when heated through the same temperature rise , In other words they have the same volume expansion coefficient , Charles’s law expresses the effect of temperature on the volume of a gas at constant pressure .
**

**Charles’s law**

**All gases have the same ****volume expansion coefficient**** , at constant pressure , so , the volume expansion coefficient ( α _{v} ) can be determined from the following relation :**

**α _{v} = Δ ( V_{ol} ) / [ ( V_{ol} )_{0°C} Δt ]**

**α _{v} = [ ( V_{ol} )_{t} − ( V_{ol} )_{0°C} ] / [ ( V_{ol} )_{0°C} Δt ]**

**The measuring unit of the volume expansion coefficient is ( Kelvin ) ^{−1} = ( K^{−1} ) .**

**The volume expansion coefficient of gas at constant pressure ( α _{v} ) is the increase in volume at constant pressure per unit volume at 0°C for rise in temperature , or it is the ratio between the increase in volume to the original volume at 0° C for 1° C rise in temperature at constant pressure .
**

**When the volume expansion coefficient of a gas under a constant pressure = ( 1/273 ) K ^{−1} , It means that the increase in volume at constant pressure per unit volume at 0° C for 1° C rise in temperature = 1/273 of the original volume .**

**To convert from Celsius to Kelvin , we use the following relation : ****T ( °K ) = t° C + 273**

**Where : ( T ) → Temperature on Kelvin scale , ****( t ) → Temperature on Celsius scale .**

**Charles’s law : At constant pressure , the volume of a given mass of gas expands by 1/273 of its original volume at 0°C per each degree Kelvin rise in temperature , or at constant pressure , the volume of fixed mass of gas is directly proportional to its temperature on Kelvin scale .**

**Charles’s law mathematical formula : V _{1} / V_{2} = T_{1} / T_{2} **

**( V _{ol} )_{1} / ( V_{ol} )_{2} = T_{1} / T_{2}**

**T _{1} = 273 + t_{1} , T_{2} = 273 + t_{2}**

**( V _{ol} )_{1} / ( V_{ol} )_{2} = 273 + t_{1} / 273 + t_{2}**

**( V _{ol} )_{1} / ( V_{ol} )_{2} = ( 1 + 1/273 t_{1 }) / ( 1 +1/273 t_{2} ) , α_{v} = 1/273**

**∴ ( V**_{ol} )_{1} / ( V_{ol} )_{2} = ( 1 + α_{v} t_{1 }) / ( 1 + α_{v} t_{2} )

_{ol})

_{1}/ ( V

_{ol})

_{2}= ( 1 + α

_{v}t

_{1 }) / ( 1 + α

_{v}t

_{2})

**If two gases are mixed at constant pressure , then **

**( V**_{ol} ) / T ( mix. ) = [ ( V_{ol} )_{1} / T_{1} ] + [ ( V_{ol} )_{2} / T_{2} ]

_{ol}) / T ( mix. ) = [ ( V

_{ol})

_{1}/ T

_{1}] + [ ( V

_{ol})

_{2}/ T

_{2}]

**Jolly’s law or pressure law**

**Jolly’s law expresses the relation between gas pressure and its temperature at constant volume , The pressure of gases increases by increasing the temperature , The increase in the pressure is constant for all gases .**

** At constant volume , the pressure of a given mass of a gas increases by increasing temperature , At constant volume equal pressures of different gases increase equally when heated to the same temperature .
**

**Pressure expansion coefficient is constant for all gases , Equal pressures of different gases increase equally when heated through the same rise in temperature because expansion coefficient for any gas at constant volume is constant . **

**At constant volume , the increase in the pressure ( Δ P ) is directly proportional to :
**

**Original pressure at 0° C ( P**_{o }) : Δ P ∝ P_{0° C}**Increase in temperature ( Δ t ) : Δ P ∝ Δ t**

**∴ Δ P ∝ P _{0° C} Δ t
**

**∴ Δ P = constant P _{0° C} Δ t**

**∴ Δ P = β**_{p} P_{0° C} Δ t

_{p}P

_{0° C}Δ t

**Where ( β _{p} ) is the pressure expansion coefficient **

** β _{p} = Δ P / ( P_{0° C} Δ t )**

**β**_{p} = ( P_{t} − P_{0° C} ) / ( P_{0° C} × Δ t )

_{p}= ( P

_{t}− P

_{0° C}) / ( P

_{0° C}× Δ t )

**The measuring unit of pressure expansion coefficient is ( Kelvin ^{−1} ) or K^{−1} . **

**The pressure expansion coefficient of a gas at constant volume ( β _{p} ) is the increase in pressure of a gas per unit pressure at 0° C when the temperature increases 1° C at constant volume . **

**Or it is the ratio between the increase in gas pressure to the original pressure at 0° C when the temperature rises 1° C at constant volume .**

**When the pressure expansion coefficient of a gas = 1/273 K ^{−1} , It means that the increase in pressure of the gas per unit pressure at 0° C when the temperature increases 1° C at constant volume = 1/273 of the original volume .
**

**The pressure expansion coefficient of a gas can be determined by knowing its pressure at t _{1} , t_{2} at constant volume from the relation :**

**P**_{1} / P_{2 }= ( 1+ β_{p}t_{1} ) / ( 1+ β_{p}t_{2} )

_{1}/ P

_{2 }= ( 1+ β

_{p}t

_{1}) / ( 1+ β

_{p}t

_{2})

**Jolly’s law or pressure law : The pressure of a given mass of gas , kept at constant volume , increases by 1/273 of its pressure at 0° C per each degree Kelvin rise in temperature , ****Or at constant volume , the pressure of fixed mass of gas is directly proportional to its temperature on Kelvin scale .**

**The absolute zero ( zero Kelvin ) by using Charles’s apparatus : ****The absolute zero is the temperature at which the volume of an ideal gas vanishes theoretically at constant pressure .**

**When the absolute zero is = − 273° C , It means that the temperature at which the volume of ideal gas vanishes theoretically at constant pressure = − 273° C . **

**The absolute zero ( zero Kelvin ) by using Jolly’s apparatus : ****The absolute zero is the temperature at which the pressure of an ideal gas vanishes theoretically at constant volume .**

** When the absolute zero is = − 273° C , It means that the temperature at which the pressure of ideal gas vanishes theoretically at constant volume = − 273° C .
**

**The temperature on Kelvin scale is always positive value while the temperature on Celsius scale may be positive or negative value .**

**General gas law**

**General gas law studies the gas behavior when changing volume , pressure and temperature of a gas together , Also explains the relation between the three variables together . **

**From Boyle’s law : V _{ol} ∝ 1/p , **

**From Charles’s law : V**

_{ol}∝ T .**∴ V _{ol} ∝ T / P , V_{ol} = constant T / P**

**P V _{ol} / T = constant**

**( P _{1} ( V_{ol} )_{1} ) / T_{1} = ( P_{2} ( V_{ol} )_{2 }) / T_{2}**

**The general gas law : The product of the volume of a fixed mass of gas and its pressure divided by its temperature on Kelvin scale equals constant value .**

**ًWhen the gas at ( STP ) , So , P = 1.013 × 10 ^{5} N/m² , T = 273°K .**

**At the change of density of a gas at constant mass , So :**

** P**_{1} / ρ_{1} T_{1} = P_{2} / ρ_{2} T_{2}

_{1}/ ρ

_{1}T

_{1}= P

_{2}/ ρ

_{2}T

_{2}

**If two gases are mixed with each other , So :**

**( P V _{ol} / T ) ( mix. ) = ( P_{1} ( V_{ol} )_{1} ) / T_{1} + ( P_{2} ( V_{ol} )_{2 }) / T_{2}**

**Gas laws , Boyle’s law and properties of gaseous materials**

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