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 :
A
362.5 kPa
B
275 kPa
C
437.5 kPa
D
550 kPa
Text Solution
Verified by Experts
The correct Answer is:
B
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"`
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