Question

Assume you are injection molding plastics parts using a polylactic acid. In the process, the resin is heated from room temperature (25 ^oC) to 200 ^oC. The cycle time is 5 second, and shot weight is 0.05 kg. Please calculate the heat input per hour of the process. The heat capacity data of PLA can be found from the excel file. The PLA used has 10, 000g/mol molecular weight (weight-average), T_g around 59.35 ^oC and melting point Tm at 160 ^oC with heat of fusion of 34 J/g. (8 pt)

T (K)	Cp (J/k/mol)
5	0.31
6	0.6
7	0.95
8	1.34
9	1.78
10	2.25
15	4.85
20	7.74
25	10.585
30	13.15
40	18.06
50	22.585
60	26.575
70	30.455
80	34.195
90	37.77
100	41.145
110	44.4
120	47.52
130	50.52
140	53.41
150	56.2
160	58.98
170	61.71
180	61.4
190	67.08
200	69.75
210	72.35
220	74.96
230	77.51
240	80.13
250	82.8
260	84.25
270	87.11
280	89.82
290	92.48
298.15	94.69
300	95.3
310	98.13
320	101.59
330	112.16
332.5	145.44	(Tg)
340	146.01
350	146.77
360	147.53
370	148.29
380	149.05
390	149.81
400	150.57
410	151.33
420	152.09
430	152.85
440	153.61
450	154.37
460	155.13
470	155.89
480	156.65
490	157.41
500	158.17
510	158.93
520	159.69
530	160.45
540	161.21
550	161.97
560	162.73
570	163.49
580	164.25
590	165.01
600	165.77

Answer 1

above values are given in the question, cycle time = 5s. shot weight = 0.05kg

=> in an hour total mass of material heated = 3600/5 * 0.05 kg = 36kg

Now, molar weight of PLA is 10kg, => 36kg = 3.6mol

now, total heat required = heat to attain melting point + heat of fusion + heat to attain injection point

Heat to attain melting point (433K):

mC​t now c value changes with temp. for PLA

therefore, total heat required H(​298-433) = 3.6*(1.85*94.69 + 10*(95.3+98.13+101.59) + 2.5*112.16 +7.5*145.44+ 10*(146.01+146.77+147.53+148.29+149.05+149.81+150.57+151.33+152.09+152.85) +3*153.61) = 71641.5J

Heat of fusion = 34*36000J = 1224000J

Heat to attain injection temperature (473) , H(433-473) =

3.6*(7*152.85+10*(153.61+154.37+155.13) +3*(155.89)) = 22207.4J

therefore total heat =71641.5J +​ ​1224000J + 22207.4J = 1317849J