Exactly one mole of nitrogen gas confined within a cylinder by a piston is heate

Question

Exactly one mole of nitrogen gas confined within a cylinder by a piston is heated from 0

Exactly one mole of nitrogen gas confined within a cylinder by a piston is heated from 0 degree C to 843 degree C at 1.00 atm. (a) Calculate the work of expansion of the gas in joules (1 J = 9.87 times 10-3 atm·L). Assume all the energy is used to do work. our response differs from the correct answer by more than 10%. Double check your calculations. J (b) What would be the temperature change if the gas were heated with the same amount of energy in a container of fixed volume? (Assume the specific heat capacity of N2 is 1.00 Your response differs from the correct answer by more than 10%. Double check your calculations. degree C

Explanation / Answer

a) pV = nRT
1 atm *V = 1 mol*0.082 L atm/K mol * 273.15
V1 = 22.39 L

p1V1/T1 = p2V2/T2
Since a piston is involved, the pressure remains constant, volume changes.
V1/T1 = V2/T2

V2 = V1*T2/T1
   = 22.39 L *1116.15 K/273.15 K
   = 91.49 L

W = p*DeltaV = 1 atm*(91.49 L-22.39 L)
             = 69.1 atm*L
            = 69.1/(9.87 x 10^-3) J
            = 7001.01 J

b)
Q = c*m*deltaT
Q = 7001.01 J
c = 1 J/gK
m = moles N2/molecular mass = 1/28 = 0.036 g

7001.01 = 1*0.036* delta T
delta T = 7001.01/0.036
        = 194472.5

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