A pistoncylinder device initially contains 065 m3 of nitroge

A piston-cylinder device initially contains 0.65 m3 of nitrogen gas at 500 kPa and 350 C. An electric heater within the device is turned on and is allowed to pass a current of 2 Amp for 15 minutes from a 120 Volt source. Nitrogen expands at constant pressure and a heat loss of 2.75 kJ occurs during the process. Determine the final temperature of the nitrogen.

Solution

Volume V = 0.65 m ³

Pressure P = 500 kPa

                  = 500 x10 ³ Pa

Tempratre T = 350 ^oC

                 = 350 + 273

                 = 623 K

Number of moles n = PV/RT

Where R = Gas constant = 8.314 J / mol K

Substitute values you get n = (500 x10 ³)(0.65)/(8.314x623)

                                          = 62.74 mol

Current i = 2 A

Time t = 15 min = 15 x 60 s

                        = 900 s

Voltage V = 120 volt

Heat given by heater Q = Vi t

                      = 120 x 2 x 900

                      = 216x10 ³ J

                                  = 216 kJ

heat lost Q \' = 2.75 kJ

Heat absorbrd by gas Q \" = Q - Q \'

                                     = 213.25 kJ

We know Q \" = nCp dT    Where Cp = Specific heat at constant pressure = 7R/2 = 3.5 R = 3.5 x8.314

From this change in temprature dT = Q\" /nCp     

                                                   = (213.25 x10 ³ )/(62.74 x3.5x8.314)

                                                   = 116.8 K

The final temperature of the nitrogen T \' = T + dT

                                                        = 623 K + 116.8 K

                                                        = 739.8 K

                                                        = (739.8 -273) ^o C

                                                        = 466.8 ^o C