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. How much work was done (in J) and how much heat was transferred?

Answer 1

if constant pressure, then

P1 = P2

1 bar = P2

At constant P

Q = dH is true

dH = n*Cp*dT

get n

n = PV/(RT) = 1*24.5/(0.08314*295) = 0.99892 mol

Cp = Cv + R = 5/2*R + R = 7/2R = 7/2*8.314 = 29.099 J/molK

Q = dH = n*Cp*(/Tf-Ti) = (0.99892)(29.099)(250-25)

Q = 6540.203 J

b)

if =P constant

W = -P*(Vf-Vi)

Vi = 24.5 L

Vf = from

V1/T1 = V2/T2

Vf = (250+273)/(25+273) * 24.5 = 42.998 = 43 L

P = 1 bar = 10^5 Pa 1 m3 = 10^3 L

W = -(1*10^5)(43-24.5)*10^-3

W = -1850 J = -1.85 kJ

W = - 1850 J =  -1.85 kJ