With what minimum pressure (in kPa), a given volume of an ideal gas `(C_(p,m)=7//2R)` originally at 400 K and 100 kPa pressure can be compressed irreversibly adiabatically in order to raise its temperature to 600 K :

Options

A. 362.5 kPa
B. 275 kPa
C. 437.5 kPa
D. 550 kPa

Answer

B

Explanation

For an adiabatic irreversible compression,
`DeltaU=w`
`thereforenC_(v,m)(T_(2)-T_(1))=-P_("ext")(V_(2)-V_(1))` here `P_("ext")=P_(2)`
`nC_(v,m)(T_(2)-T_(1))=-P_(2)[(nRT)/(P_(2))-(nRT_(1))/(P_(1))]`
`implies (5)/(2)R(T_(2)-T_(1))=-P_(2)xxR[(T_(2))/(P_(2))-(T_(1))/(P_(1))]`
`implies" "P_(2)=275 " kPa"`