Basic Mechanical Engineering (3110006)

Specific heat at Constant volume:

Specific heat at Constant pressure:

Adiabatic index:

Relationship between specific heats in form of characteristic gas constant:

• At constant pressure, from the 1st law of thermodynamics, ${\mathrm{Q}}_{1-2} = \mathrm{dU} + {\mathrm{W}}_{1-2}$
   
• For constant pressure process, the heat transferred, ${\mathrm{Q}}_{1-2} = {\mathrm{mC}}_{\mathrm{p}}\mathrm{dT}$
   
  Change in internal energy is, $\mathrm{dU} = {\mathrm{mC}}_{\mathrm{v}}\mathrm{dT}$
   
  Work done is given by, ${\mathrm{W}}_{1-2} = \mathrm{p} \mathrm{dV}$
   
• Substitute the value of ${\mathrm{Q}}_{1-2} , \mathrm{dU}$ and ${\mathrm{W}}_{1-2}$ in above equation, we get
   
  ${\mathrm{mC}}_{\mathrm{p}}\mathrm{dT} = {\mathrm{mC}}_{\mathrm{v}}\mathrm{dT} + \mathrm{pdV}$
   
• From a characteristic gas equation, $\mathrm{pV} = \mathrm{mRT}$
   
  ${\mathrm{mC}}_{\mathrm{p}}\mathrm{dT} = {\mathrm{mC}}_{\mathrm{v}}\mathrm{dT} + \mathrm{mRdT}$
   
  ${\mathrm{C}}_{\mathrm{p}} = {\mathrm{C}}_{\mathrm{v}} + \mathrm{R}$
   
  $\mathrm{R} = {\mathrm{C}}_{\mathrm{p}} - {\mathrm{C}}_{\mathrm{v}}$