The molar heat capacities for carbon dioxide at 298.0 K are shown below. C_v = 2

Question

The molar heat capacities for carbon dioxide at 298.0 K are shown below. C_v = 28.95 J K^-1 mol^-1 C_p = 37.27 J K^-1 mol^-1 The molar entropy of carbon dioxide gas at 298.0 K and 1.000 atm is 213.64 J K^-1 mol^-1. Calculate the energy required to change the temperature of 1.000 mole of carbon dioxide gas from 298.0 K to 348.0 K, both at constant volume and at constant pressure. Calculate the molar entropy of CO_2(g) at 348.0 K and 1.000 atm. Calculate the molar entropy of CO_2(g) at 348.0 K and 1.189 atm. One mole of an ideal gas is contained in a cylinder with a movable piston. The temperature is constant at 73 degree C. Weights are removed suddenly from the piston to give the following sequence of three pressures. What is the total work (in joules) in going from the initial to the final state by way of the preceding two steps? What would be the total work if the process were carried out reversibly?

Explanation / Answer

ANSWER

(1) Energy required to raise the temperature from 298K to 348K

(i)

(a) At constant volume

E = Cv X m X T

E = 28.95 X 1 X (348.0 - 298) = 1447.5Jmol-1 = 1.4475KJmol-1

(b) At constant pressure

E = 37.27 X 1 X (348.0 - 298) = 1.8635KJmol-1

(ii)

(a) S = nCv X 2.303logT2/T1 n = no.of moles

S = (S2 - S1) = 28.95 X 2.303log348/298 = 4.467

(S2 - S1) = 4.467

S2 = S1 + 4.467 = 213.64 + 4.467 = 218.12 JK-1mol-1

(b) (S2 - S1) = nCp ln (T2/T1) - nRln(P2/P1)

(S2 - 213.64) = 37.27 X ln (348/298) - 8.314 ln(1.189/1) = 5.75 - 1.43 = 4.31

S2 = 213.64 + 4.31 = 217.95 J/Kmol

Dear candidate You have asked two questions as per guidelines one question one time

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