Question

Gummie!!!!
Derive the mathematical expression for :
(i) Charles' law.......​

Answer 1

★ Charles' Law :

It is a law stating that the volume of an ideal gas at constant pressure is directly proportional to the absolute temperature.

★ Derivation :

according to law ,

$V \propto T$ (Pressure is constant)

We know that, when proportionality is removed then a constant is added . (K is the constant)

V = KT

${\purple{\boxed{K = \frac{V}{T}}}}$

constant always remains same.

for 2 gases ,

$1^{st}\: gas - volume = V_{1} , temperature = T_1$

$2^{nd} \: gas - volume = V_{2} , temperature = T_2$

$K = \frac{V_1}{T_1}$

$K = \frac{V_2}{T_2}$

${\pink{\boxed{\therefore \: \frac{V_1}{T_1} = \frac{V_2}{T_2}}}}$

hence , derived .

★ Additional Information :

Formula of Gay - lussac law -

${\pink{\boxed{\frac{P_1}{T_1} = \frac{P_2}{T_2} \: (Volume\: is \: constant)}}}$

Formula of Boyle's Law -

${\pink{\boxed{\frac{P_1}{d_1} = \frac{P_2}{d_2} \: (Temperature \: is \: constant)}}}$

Ideal gas equation :

${\pink{\boxed{PV = nRT}}}$

P - pressure

V = volume

n = number of moles

T = temperature

R = Ideal gas constant

$\left(R = 0.0821 \: \frac{L . atm}{mol.K}\right)$

Answer 2

Answer:

Charles law also sometimes referred to as the law of volumes gives a detailed account of how gas expands when the temperature is increased. Conversely, when there is a decrease in temperature it will lead to a decrease in volume.

When we compare a substance under two different conditions, from the above statement we can write this in the following manner:

V2/V1=T2/T1

OR

V1T2=V2T1

This above equation depicts that as absolute temperature increases, the volume of the gas also goes up in proportion.

In other words, Charle’s law is a special case of the ideal gas law. The law is applicable to the ideal gases that are held at constant pressure but the temperature and volume keep changing.

As we are aware of the fact that, at constant pressure, the volume of the fixed amount of the dry gas is directly proportional to absolute temperature according to Charle’s law. We can represent the statement in the following manner.

V∝T

Since V and T are varying directly, we can equate them by making use of the constant k.

V/T=constant =k

In this, the value of k depends on the pressure of the gas, the amount of the gas and also the unit of the volume.

V*T=k——-(1)

Let us consider V1 AND T1 to be the initial volume and the temperature respectively of an ideal gas.

Then we can write equation (1) as

V1/T1=k——-(2)

After it lets change the temperature of the gas to T2. Alternatively, its volume changes to V2 then we can write

V2/T2=k——–(3)

Equating the above equations that is equation 2 and 3, we get

$\frac{v1}{t1} = \frac{v2}{t2}$

OR

$v1t2 = v2t1$

You are unaware of the fact that, on heating up a fixed amount of gas, that is, by increasing the temperature the volume also increases. Similarly lowering the temperature, the volume of the gas decreases. And at 0-degree centigrade, the volume of the also increases by 1/273 of its original volume for a unit degree increases in temperature.