(Solved): A pseudo adiabatic process is not a polytropic process, 3. A pseudo adiabatic process is not a polyt ...

3. A pseudo adiabatic process is not a polytropic process, but it may be approximated as such over a Limited range of pressure and temperature. Show that in a pseudo adiabatic process at $270\mathrm{K}$ and $80\mathrm{kPa}$, pressure and specific volume are related by ${\mathbf{pa}}^{\mathbf{n}}=$ const., where $\mathrm{n}$ has the value 1.23 . Show further that $\mathbf{n}$ deviates only $5\%$ from this value as the temperature changes by $\pm 10\mathrm{K}$ about $270\mathrm{K}$ and the pressure changes by $\pm 10\mathrm{kPa}$ about $80\mathrm{kPa}$.