Question

define boyle's law with its mathematical expression

Answer 1

Hi,

Here is your answer,

                                             BOYLE'S LAW

Robert Boyle studied the relationship between volume and pressure of a gas keeping the temperature constant. This relationship is named after him as Boyle's Law.

Boyle's law state that at constant temperature the volume of certain mass of a gas is inversely proportional to its pressure.

 V α 1/P at a constant temperature, where V is the volume and P is the pressure. Introducing Proportionality constant K.

 V = K/P or PV = K

→ At constant temperature, the product of pressure and volume of a given mass of gas is constant. If P₁ and P₂ are the initial and final pressures, V₁ and V₂ are initial and final volumes respectively at constant temperature.

                                   P₁V₂ = P₂V₂

→ When pressure of gas is plotted against its volume at constant temperature for a fixed mass of gas, we get curves. The shape of the Boyle's Law curve is rectangular hyperbola.

→ Since the temperature is constant, Boyle's Law curves are called isotherms. When the product of pressure and volume is plotted against the pressure or volume, a straight line parallel to the pressure or volume, a straight line parallel to the pressure or volume axis is obtained.

NOTE:- Before deriving the Boyle's Law we need to derive Gas law from kinetic gas Equation.

Let's start deriving the ''Gas law from kinetic gas Equation.''

Change in momentum = Pbefore - Pafter

                = mμx - (-mux)

                = 2mux ------------->(1)

 Velocity = Distance/time

 = 2L/Δt = Δt = 2L/velocity = 2L/Ux --------------->(2)


Force = change in momentum/Δt = 2mux/2L/μx = mu²/L  ------------>(3)

Pressure = Force/area 

          = mu²x/L × 1/area

         = mux²/L × 1/L²

          = mu²x/L²

      P = mu²x/V

Now, Total Velocity u² = u²x  + u²y + u²z

       = (Ux = Uy = Uz)

      = U² = U²x + U²x + U²x

       = U² = 3U²x

      = U²/3 = U²x --------->(4)

→ P = mu²x/V

→ P = mu²/3v

→ PV = 1/3mu²

Here, U and C ---> Velocity 

→ PV = 1/3mc²  → Kinetic Energy Gas Law

Now, we will derive Boyle's Law

→ PV = 1/3mc²

PV = 2/3×2 mc²

→PV = 2/3 (1/2mc²)

→ PV = 2/3 K.T

→ PV = 2/3 K.T

→ PV = Constant 


Hope it helps you !

Answer 2

Answer: click on the attachment

Please select my answer as BRAINLIST

Explanation: