• # question_answer 56) With what minimum pressure in Kpa of given volume of an ideal gas $\left( Cp\,\,=\,\,\frac{7}{2}R \right)$ originally   at 400 K and 100 kPa pressure, be adiabatically compressed in order to raise its temperature to 600 K- A) 362.5 kpa                     B) 275 kpaC) 437.5 kpa                     D) 550 kpa

For an adiabatic irrereversible compression, $\Delta E\,\,=\,\,W$ $\therefore \,\,\,n{{C}_{v}}\left( {{T}_{2}}-{{T}_{1}} \right)=-\,{{P}_{ext}}\left( V{{ & }_{2}}-{{V}_{1}} \right)$ $\therefore \,\,\,n{{C}_{v}}\left( {{T}_{2}}-{{T}_{1}} \right)=-\,{{P}_{2}}\,\left( \frac{nR{{T}_{2}}}{{{P}_{2}}}-\frac{nR{{T}_{1}}}{{{P}_{1}}} \right)$ $=\,\,n\times \frac{5}{2}R\,({{T}_{2}}-{{T}_{1}})\,\,=\,\,-{{P}_{2}}\times nR\,\left[ \frac{{{T}_{2}}}{{{P}_{2}}}-\frac{{{T}_{1}}}{{{P}_{1}}} \right]$ $=\,\frac{5}{2}\times \,\,(600-400)\,\,=\,\,-{{P}_{2}}X\,\left[ \frac{600}{{{P}_{2}}}-\frac{400}{100} \right]$ ${{P}_{2}}\,\,=\,\,275\,Kpa.$