## Isobaric Process – Heat and Energy

**Isobaric Process – Heat and Energy**

The classical form of the first law of thermodynamics is the following equation:

**dU = dQ – dW**

In this equation dW is equal to **dW = pdV** and is known as the boundary work.

In an isobaric process and the ideal gas, **part of heat added** to the system will be used to **do work** and **part of heat** added will increase the **internal energy** (increase the temperature). Therefore it is convenient to use the **enthalpy** instead of the internal energy.Since ** H = U + pV**, therefore

*and we substitute*

**dH = dU + pdV + Vdp***into the classical form of the law:*

**dU = dH – pdV – Vdp****dH – pdV – Vdp = dQ – pdV**

We obtain the law in terms of enthalpy:

*dH = dQ + Vdp*

or

*dH = TdS + Vdp*

In this equation the term * Vdp* is a

**flow process work.**This work,

*, is used for*

**Vdp****open flow systems**like a

**turbine**or a

**pump**in which there is a

**“dp”**, i.e. change in pressure. There are no changes in control volume. As can be seen, this form of the law

**simplifies the description of energy transfer**.

**At constant pressure**, the

**enthalpy change**equals the

**energy**transferred from the environment through heating:

**Isobaric process (Vdp = 0):**

**dH = dQ → Q = H**_{2}** – H**_{1}

**At constant entropy**, i.e. in isentropic process, the **enthalpy change** equals the **flow process work** done on or by the system.

**Isentropic process (dQ = 0):**

**dH = Vdp → W = H**_{2}** – H**_{1}

It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i.e. in Brayton cycle and Rankine cycle.

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