Question

8) Some fish have swim bladders to control buoyancy. Assume Nemo 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) eqn., b) 16.6J, c) 207°C, 40J, 23.9J]

a) What is the minimum amount of work the Nemo 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 Nemo do to squish his air bladder?

c) In a crash dive to get away from a shark, Nemo squishes 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 part b, how much work has he done on his air bladder? To figure out which model to use consider the heat flow during this process and decide if you should approximate the dive as an adiabatic or isothermal system (Justify your answer)

Answer 1

a)Minimum work will be done in an isobaric process- constant pressure.

The work is given by, W=P*(V2-V1)

b)n=0.01 V1=V V2=V/2 T=288 K

It is an isothermal process

W=nRT ln(V2/V1)

R=8.314

c)The process should be modelled as adiabatic since it is a sudden process and there is no time for heat transfer to take place.

W=P1V1-P2V2/(1-n)

n=Cp/Cv for air=7/5=1.4

P1=1 atm

using P1*V1=nRT, we can find V1. Hence V2 will also become known. Substitute in equations for W to get the answer.