We heat up 2.43 mol of some gas from 21.7 degrees C to 139.0 degrees C, holding

Question

We heat up 2.43 mol of some gas from 21.7 degrees C to 139.0 degrees C, holding the pressure constant. The molar specific heat at constant volume for this gas is Cv=31.41 J/mol.K. (a) Assuming that this gas behaves like an ideal gas, find the value of the molar specific heat (J/mol.K) at constant pressure Cp. (b) Find the amount of heat (J) that flows into the gas. (c) Find the amount of work (J) done on the gas. (d) Find the change of internal energy (J) of the gas. Be sure to include the correct signs on the answers.

Explanation / Answer

The number of moles n = 2.43 moles

The initial temperature Ti = 21.7 deg + 273.15 = 294.85 K

The final temperature Tf = 139 + 273.15 = 412.15K

The molar specific heat at constant volume Cv = 31.41 J/mol K

(a) The molar specific heat at constant pressure Cp = Cv + R

                               Cp = 31.41 + 8.31 = 39.72 J/mol.K

(b) The amount of heat flows into gas

                Q = nCp T

                    = (2.43)(39.72)(117.3)

                    = 11321.75 J

(c) The amount workdone on the gas

              W = nRT

                  = (2.43)(8.31)(117.3)

                  = 2368.67 J

since work is done on the gas so W = - 2368.67J

(d) The change in internal energy of the gas

            E = nCv T

                 = (2.43)(31.41)(117.3)

                 = 8953.1 J

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