Name: Absolute Zero and Third Law of Thermodynamics
Uploaded: 2019-07-19
Duration: 20 min
Description: In this video, you will learn what absolute zero and the third law of thermodynamics is. You will also learn about the significance of the third law of therm...

Question

Starting with the thermodynamic relationships,

ΔU = q - PΔV

and

H = U + PV

, derive the relationship

ΔH = q_{p}

.

Accepted Answer

For this the process is to be carried out at constant pressure, the work of expansion is given by,

$w = - P ∆ V - - - - - (1) .$

Where,

$∆ V$ is the change in the volume.

$P$ is the constant pressure.

From first law of thermodynamics, we have

$q = ∆ E - w - - - - - (2) .$

Where,

$q$ is the heat absorbed by the system.

$∆ E$ is the change in the internal energy.

$w$ is the work done by the system.

Therefore, substituting the values of ‘ $w$ ' from equation $(1)$ in equation $(2)$ we get,

$q = ∆ E - w . q = ∆ E - (- P ∆ V) . q = ∆ E + P ∆ V .$

Therefore, heat at constant pressure can be calculated as,

$q_{p} = ∆ E + P ∆ V - - - - - (3) .$

Now, if the internal energy $E$ of the system increases from $E_{1} \to E_{2}$ .

Therefore, $∆ E = E_{2} - E_{1} - - - - - (4) .$

If, the volume of system also increases from $V_{1} \to V_{2}$ .

$∆ V = V_{2} - V_{1} - - - - - (5) .$

Now putting the values of $∆ E$ and $∆ V$ in equation $(3)$ .

$q = ∆ E + P ∆ V . q = (E_{2} - E_{1}) + P (V_{2} - V_{1}) . q = (E_{2} + {PV}_{2}) - (E_{1} + {PV}_{1}) - - - - - (6) .$

Where,

$E, P$ and $V$ are state functions.

The physical quantity, $E + PV = H$ . i.e., heat Content.

Now, for enthalpy Change $∆ H = H_{2} - H_{1} .$

Where,

$H_{2}$ is the enthalpy of final state, $H_{2} = E_{2} + {PV}_{2}$ .

$H_{1}$ is the enthalpy of the Initial state, $H_{1} = E_{1} + {PV}_{1} .$

Now, putting the values of $H_{2}$ and $H_{1}$ in equation $(6)$ , we have $q_{p} = ∆ H .$

Starting with the thermodynamic relationships, $ΔU = q - PΔV$ and $H = U + PV$ , derive the relationship $ΔH = q_{p}$ .

Important Questions on Thermodynamics

Learn and Prepare for any exam you want !

Starting with the thermodynamic relationships, ΔU = q – PΔV and H = U + PV, derive the relationship ΔH = qp.

Important Questions on Thermodynamics

Learn and Prepare for any exam you want !

Starting with the thermodynamic relationships, $ΔU = q - PΔV$ and $H = U + PV$ , derive the relationship $ΔH = q_{p}$ .