A cylinder if fitted with a floating piston oriented horizontally (the air is th

Question

A cylinder if fitted with a floating piston oriented horizontally (the air is the system and by having a floating piston it maintains constant pressure).

It contains 24.5 L of air at 25.0C and 1 bar pressure. The system is then heated to 250.0C.

Air can be considered a diatomic gas and therefore would have a Cv = 5R/2, where R is the ideal gas constant. Also for gases Cp = Cv +R.

If you make assumptions to solve they must be consistent with this information given (for example: do not look up a new specific heat for air, different than what I defined it as)

(a) How much air is in the system (in standard moles = g-moles)?

(b) What is the change in kinetic energy (in J)?

(c) What is the change in potential energy(in J)?

(d) What is the change in internal energy(in J)?

(e) What is the change in enthalpy (in J)?

(f) How much work was done (in J)? Need correct sign

(g) How much heat was transferred? Need correct sign

Explanation / Answer

a)

PV = nRT

n = PV/(RT) = 1*24.5/(0.0831*298) = 0.989347 mol

b)

change in Kinetic energy -->

KE = 3/2*k*T

K = bolztman constnat = 1.38*10^-23

dE = Ek2 - Ek1 = 3/2*k*T2 - 3/2*k*T1 = (3/2* 1.38*10^-23) ( 250-25) = 4.65*10^-21

(c) What is the change in potential energy(in J)?

change in potential energy = change in kinetic energy

d)

internal energy

dU = U2-U1 = n*Cv*(Tf-Ti) = 0.989347 *5*8.314/2 * (250-25) = 4626.804913J

e)

change in enthalpy

dH = H2-H1 = n*Cp*(Tf-Ti) = 0.989347 *(5*8.314/2 + 8.314)* (250-25) = 6477.52 J

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