Some fish have swim bladders to control buoyancy. Assume a fish compresses his swim bladder from an initial state (T1, P1, V1, n) to a final state (T2, P2, V2, n) assuming air is an ideal gas.
a.) What is the minimum amount of work the fish must do to compress his swim bladder? Derive the appropriate equation.
b.) If the bladder contains 0.01 moles of air and it is compressed to half its original volume at 288K, how much work must the fish do to squish his air bladder?
c.) In a crash dive to get away from a shark, the fish squisehes his air bladder as hard as he can to its final state. If the original pressure was 1 atm and the same conditions as his dive in (b) how much work has he done on his air bladder? To figure out how to calculate this consider the heat flow during this process and decide if you should approximate the dive as an adiabatic or isothermal system. (Justify you answer)