A vertical cylinder with a heavy piston contains air at a temperature of 300 K.

Question

A vertical cylinder with a heavy piston contains air at a temperature of 300 K. The initial pressure is 280 kPa and the initial volume is 0.350 m3. Take the molar mass of air as 28.9 g/mol and assume that CV = 5R / 2.

(a) Find the specific heat of air at constant volume in units of kJ/kg·K.

(b) Calculate the mass of the air in the cylinder.

(c) Suppose the piston is held fixed. Find the energy input required to raise the temperature of the air to 700 K.

(d) Assume again the conditions of the initial state and that the heavy piston is free to move. Find the energy input required to raise the temperature to 700 K.

Explanation / Answer

(a) Cv= 5R/2 = 5(8.314)/2 = 20.875 J/mol*K

Cv= (20.785 J/mol*K)/(.0289 kg/mol) = .719 kJ/kg*K

(b)since m=Mn, m=M*PV/RT = (.0289)[(280E3)(.35)]/[8.314*300]

m= 1.1355 kg

(c) Q=m*Cv*T (Plug in values)

(d) Cp=Cv+R 5R/2 +R = 7R/2 = 7/2 * 2/5 * 5R/2 = 7Cv/5 = 7(719.2)/5 = 1006.88 J/kg*K = Cp

Q=m*Cp*T (plug in values)

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