Question

please proof that CP - CV= R

Answer 1

let CP be R
suppose CV is zero
now
R - 0=R
hence proved....

Answer 2

Cp - Cv = R

This is otherwise called Meyer's Relation.

dQ’  = dU + dW

Since the expansion takes place at constant pressure,

dQ ′ = CpdT

∴ CpdT = CvdT + dW                     …... (2)

Work done, dW = force × distance = = P × A × dx

dW = P dV (since A × dx = dV, change in volume)

∴ CpdT = CvdT + P dV             …... (3)

The equation of state of an ideal gas is

PV = RT

Differentiating both the sides

PdV = RdT              …... (4)

Substituting equation (4) in (3),

CpdT = CvdT + RdT

Cp = Cv + R

Therefore,

Cp - Cv = R.

Please mark my answer as brainliest.