Question

derive 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

Mayers formula:

Cp - Cv = R

Derivation:

ΔU = ΔQ + ΔW
ΔU = Cv ΔT (At pressure is constant)
ΔQ = Cp ΔT (At pressure is constant)
ΔW = -P ΔV (Negative since the calculation been complete)
Pv = RT (1 mole of gas)

Because of pressure is constant, R is also constant
Change in V will make change in T
PΔV = R ΔT
Cv ΔT = CpΔT - RΔT
Divided by ΔT
Cv = Cp - R
R is Subject
Cp - Cv = R
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