1 mole of diatomic ideal gas at 300 K and 1 atm is heated at

1 mole of diatomic ideal gas at 300 K and 1 atm is heated at constant volume to 400 K. Calculate W,Q,deltaU, and deltaH in Joules.

Solution

Number of moles n = 1

Initial temprature T = 300 K

Initial pressure P = 1 atm

                         = 1.01 x10 5 Pa

Final temprature T \' = 400 K

Initial volume V = nRT / P

Where R = Gas constant = 8.314 J / mol K

Substitute values you get V = ( 1 x 8.314 x300) /(1.01 x10 ⁵ )

                                         = 0.02469 m ³

Work done at constant volume W = 0        Since there is no change in volume in this process.

Heat Q = nCp (T \' - T )

Where Cp = Specific heat at constant volume

               = (7/2)R

               = 3.5 x8.314

Substitute values you get Q = 1 x3.5x8.314x(400-300)

                                          = 2909.9 J

Change in internal energy dU = nCv (T \' - T )

Where Cv = Specific heat at constant volume

               = (5/2)R

               = 2.5 x8.314

Substitute values you get dU = 1 x2.5x8.314x(400-300)

                                          = 2078.5 J