Energy Balance

Based on the 1st law, more specific equations are derived on a case by case basis.

Transient state

When a thermodynamic system is changing with time.

Steady state

When a thermodynamic system stays constant with time. Net energy change in the system is zero.

For closed systems

$$\text{Net energy transfer to the system} = \text{Net increase in system's total energy} Q - W = \Delta E_{\text{sys}}$$

For open systems

Total specific energy of a flow system:

$$\theta = h + \frac{1}{2}C^2 + gz$$

Here:

• $\theta$ - total specific energy
• $h = u + P\neu$ - enthalpy
• $u$ - specific internal energy
• $P\neu$ - specific flow work
• $C$ - velocity of the flow
• $g$ - gravatitaional acceleration
• $z$ - elevation of the flow system

$$Q - W + m_{\text{in}}\theta_{\text{in}} - m_{\text{out}}\theta_{\text{out}} = \Delta E_{\text{sys}}$$

Here:

• $Q$ - heat transfer
• $W$ - work transfer
• $m_{\text{in}}$ - mass flow rate of the inlet
• $\theta_{\text{in}}$ - total specific energy of the inlet
• $m_{\text{out}}$ - mass flow rate of the outlet
• $\theta_{\text{out}}$ - total specific energy of the outlet
• $\Delta E_{\text{sys}}$ - change in total energy of the system

Steady flow energy equation (SFEE)

$$q - w = (h_e - h_i + \frac{1}{2}(C_e^2 - C_i^2) + g(z_e - z_i))$$

Here:

• $q$ - specific heat transfer
• $w$ - specific work transfer
• $h_e, h_i$ - specific enthalpy at the outlet and inlet
• $C_e, C_i$ - flow velocity at the outlet and inlet
• $g$ - gravitational acceleration
• $z_e,z_i$ - elevation at the outlet and inlet