The pressure P_(1) and density d_(1) of a diatomic gas (gamma = 7//5)change to P_(2) and d_(2) during an adiabatic opertation. If (d_(2))/(d_(1)) = 32, find (P_(2))/(P_(1)).

The pressure P_(1) and density d_(1) of a diatomic gas (gamma = 7//5)c

1.	The pressure P_(1) and density d_(1) of a diatomic gas (gamma = 7//5)change to P_(2) and d_(2) during an adiabatic opertation. If (d_(2))/(d_(1)) = 32, find (P_(2))/(P_(1)).
Answer» Solution :In an adiabatic operation, `P_(1)V_(1)^(GAMMA) = P_(2)V_(2)^(gamma)` `:. (P_(2))/(P_(1)) = ((V_(1))/(V_(2)))^(gamma) = ((m)/(d_(1)) XX (d_(2))/(m))^(gamma) = ((d_(2))/(d_(1)))^(gamma)` `:. (P_(2))/(P_(1)) = (32)^(7//5) = (2^(5))^(7//5) = 2^(7) = 128 :. (P_(2))/(P_(1)) = 128`.