Question

derive the mayor's formula

Answer 1

⭕️let one gram mole of ideal gas enclosed in cyclinder fitted with piston frictionless then P,V,T== initial pressure,volume and temperature of the gas respectively. 




✔️✔️✔️Derivation :-

✔️✔️Use the first law of thermodynamics 

dQ=dU + pdv

✔️✔️specific heat of a gas at constant volume

Cv = (dQ / dT)v


Cv = dU / dT ➖➖➖➖➖➖➖➖[1]


✔️✔️specific heat capacity at constant pressure

Cp = (dQ / dT)p

Cp = dU + Pdv / dT

Cp = dU / dT + P(dV / dT)


Cp = Cv + Pdv / dT (using 1st) ➖➖➖➖[2]


By applying ideal gas in [1] for 1 mole

PV = nRT

PV = (1)RT

PV = RT

P dv / dt = R dT / dt

Pdv = RdT

P(dv / dT) =R


Putting in [2] we get; 


Cp - Cv = R.

proved !!!


$\huge\bf{\red{\mathfrak{thank \: you :)}}}$

Answer 2

Heyy Buddy❤

Here's your Answer...

Mayor 's Relationship:
By using 1st law of thermodynamics,

dQ=dU + pdv

If specific heat of a gas at constant volume
Cv = (dQ / dT)v

Cv = dU / dT...................(1st)

If specific heat capacity at constant pressure
Cp = (dQ / dT)p

Cp = dU + Pdv / dT

Cp = dU / dT + P(dV / dT)

Cp = Cv + Pdv / dT(using 1st) ........................(2)

By applying ideal gas equation for 1 mole
PV = nRT

PV = (1)RT

PV = RT

P dv / dt = R dT / dt

Pdv = RdT

P(dv / dT) =R

Putting dis value in eqn 2nd we get,

Cp - Cv = R
✔✔✔