Question

Derive the formula of Gas Equation.​

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$

GAS EQUATION :

Influence of simultaneous change in temperature and pressure on volume of a given mass of a gas is called Gas Equation.

From Boyle's law,

$\sf{V \propto \: \frac{1}{P} \: \: (at \: constant \: temp.) \rightarrow [1]}$

From Charles law,

$\sf{V \propto T \: \: \: \: \: \: (at \: constant \: pressure \: ) \:\rightarrow \: [2]}$

From [1] and [2] , we get

$\sf{V \propto \frac{T}{P} }$

$\sf{V =K \: \frac{T}{P} } \: \: \: \: \: \: \: (k = constant)$

$\sf{ \frac{PV}{T} = K}$

So,

$\sf{ \frac{ P_{1} \: V_{1} }{T_{1}} = K}$

and

$\sf{ \frac{ P_{2} \: V_{2} }{T_{2}} = K}$

$\boxed{ \therefore \: \sf{\frac{ P_{1} \: V_{1} }{T_{1}} = \frac{ P_{2} \: V_{2} }{T_{2}}}}$

Answer 2

ANSWER :

Formula of Gas Equation :

☆ P1V1/ T1 = P2V2/ T2