105 Pa, and the initial volume is 0.445 m3. Take the molar mass of air as 28.9 A

Question

105 Pa, and the initial volume is 0.445 m3. Take the molar mass of air as 28.9 A vertical cylinder with a heavy piston contains air at 315 K. The initial pressure is 2.85 g/mol and assume Cys R 5 . (a) Find the specific heat of air at constant volume in units of /kg·°C. /kg c (b) Calculate the mass of the air in the cylinder. kg (c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 730 K. kJ (d) Assume again the conditions of the initial state and assume the heavy piston is free to move. Find the energy input required to raise the temperature to 730 K. kJ

Explanation / Answer

(A) R = 8.314 J/mol K

1 mol = 28.9 g = 0.0289 kg

R= (8.314 / 0.0289) J/kg deg C

R = 287.68 J/kg degC

Cv = 5 R / 2 = 719.2 J/kg degC

(b) P V = n R T

(2.85 x 10^5) (0.445) = n (8.314) (315)

n = 48.4 mol

mass = 48.4 x 28.9 = 1400 g Or 1.4 kg

(c) Q = m Cv deltaT

= 1.4 x 719.2 x (730 - 315)

= 418 x 10^3 J

= 418 kJ

(d) now Cp = Cv + R = 7 R / 2

Q = (48.4)(3.5 x 8.314) (730 - 315)

Q = 584.5 x 10^3 J

Q = 584.5 kJ

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