Question

Deduce the relation between Cp and Cv.

Answer 1

Answer:

Cp-Cv =nR

Explanation:

this is the answer.hope it helps

Answer 2

Relationship between $\bold{C_p}$ and $\bold{C_v}$ for an Ideal Gas:

The moral heat capacity of the gas at constant volume is denoted as $\bold{C_v}$.

The molar heat capacity of the gas at constant pressure is denoted as $\bold{C_P}$.

The amount of heat transfer in ideal gas is given by the formula:

$\bold{Q = n C \Delta T}$

At constant pressure P, heat transfer is given as:

$\bold{Q_p = n C_p \Delta T}$

$\bold{Q_p = n C_p \Delta T = \Delta H \longrightarrow (1)}$

∆H is change in enthalpy

Now, at constant volume V, heat transfer is given as:

$\bold{Q_v = n C_v \Delta T}$

$\bold{Q_v = n C_v \Delta T = \Delta U \longrightarrow (2)}$

∆U is change in internal energy

We know that for one mole (n=1) of an ideal gas,

$\bold{\Delta H = \Delta U + \Delta (pV ) = \Delta U + \Delta (RT) = \Delta U + R \Delta T}$

Therefore, $\bold{\Delta H = \Delta U + R \Delta T}$

Where R is gas constant

Substituting the values of ∆H and ∆U from equation (1) and (2), we get,

$\bold{C_p \Delta T = C_v \Delta T + R \Delta T}$

$\bold{C_p = C_v + R}$

Thus,

$\bold{C_p - C_v = R}$