Thermodynamic Processes and Formulas

Isobaric Process

• Process equation:
  $p = \text{const}$
• Graphical representation: Represented as a horizontal straight line in the $p, v$ diagram.

Isochoric Process

• Process equation:
  $v = \text{const}$
• Graphical representation: Represented as a vertical straight line in the $p, v$ diagram.

Isothermal Process

• Process equation ($T = \text{const}$):
  $p<em>1 \cdot v</em>1 = p<em>2 \cdot v</em>2$
• Internal energy change:
  $\Delta u = 0$
• Heat and work relation:
  $q<em>{1,2} = l</em>{1,2}$
• Heat and work calculation:
  $q<em>{1,2} = l</em>{1,2} = R \cdot T \cdot \ln\left(\frac{v<em>2}{v</em>1}\right)$
• Quantities and units:
  • $R$: specific gas constant ($\text{J}/(\text{kg}\cdot\text{K})$)
  • $T$: constant absolute temperature ($\text{K}$)
  • $v<em>1, v</em>2$: specific volumes ($\text{m}^3/\text{kg}$)

Adiabatic Process

• Process condition ($q = 0$):
  $p \cdot v^{\kappa} = \text{const}$
• Specific work:
  $w<em>{1,2} = c</em>v \cdot (T<em>1 - T</em>2)$
• Quantities and units:
  • $\kappa$: adiabatic index ($\kappa = 1.4$ for air)
  • $c_v$: specific heat capacity at constant volume ($\text{J}/(\text{kg}\cdot\text{K})$)
  • $T<em>1, T</em>2$: initial and final absolute temperatures ($\text{K}$)
  • $w_{1,2}$: work performed by $1\,\text{kg}$ of gas ($\text{J}/\text{kg}$)

Polytropic Process

• General process equation:
  $p \cdot v^n = \text{const}$
• Polytropic exponent:
  $1 < n < 1.4$ (for air, determined experimentally)
• Heat exchanged:
  $q<em>{1,2} = c</em>v \cdot \left(\frac{n - \kappa}{n - 1}\right) \cdot (T<em>2 - T</em>1)$
• Work performed:
  • Evaluated as the area under the curve in the $p, v$ diagram.