Question

complete the table below
input work (j) output work (j) heat lost (j) efficiency
872 705
321 147
746 465
998 360
725 126
782 418
429 399
820 702
525 341
964 222
928 801
32 151
841 608
597 622
989 901
303 0.111
480 0.635
846 0.167
480 0.547

Explanation:

Step1: Calculate heat lost

Heat lost = Input work - Output work.
For the first row: \(872 - 705=167\)
For the second row: \(321 - 147 = 174\)
For the third row: \(746-465 = 281\)
For the fourth row: \(998 - 360=638\)
For the fifth row: \(725-126 = 599\)

Step2: Calculate efficiency

Efficiency \(=\frac{\text{Output work}}{\text{Input work}}\)
For the first row: \(\frac{705}{872}\approx0.809\)
For the second row: \(\frac{147}{321}\approx0.458\)
For the third row: \(\frac{465}{746}\approx0.623\)
For the fourth row: \(\frac{360}{998}\approx0.361\)
For the fifth row: \(\frac{126}{725}\approx0.174\)

Step3: Calculate output work (for rows with heat lost given)

Output work = Input work - Heat lost
For the sixth row: \(782-418 = 364\)
For the seventh row: \(429 - 399=30\)
For the eighth row: \(820-702 = 118\)
For the ninth row: \(525-341 = 184\)
For the tenth row: \(964-222 = 742\)

Step4: Calculate input work (for rows with output work and heat lost given)

Input work = Output work + Heat lost
For the eleventh row: \(928 + 801=1729\)
For the twelfth row: \(32+151 = 183\)
For the thirteenth row: \(841+608 = 1449\)
For the fourteenth row: \(597+622 = 1219\)
For the fifteenth row: \(989+901 = 1890\)

Step5: Calculate output work (for rows with efficiency given)

Output work = Input work×Efficiency
For the sixteenth row: \(303×0.111 = 33.633\approx34\)
For the seventeenth row: \(480×0.635 = 304.8\approx305\)

Step6: Calculate heat lost (for rows with efficiency given)

Heat lost = Input work - Output work
For the sixteenth row: \(303 - 34=269\)
For the seventeenth row: \(480-305 = 175\)

Step7: Calculate input work (for rows with output work and efficiency given)

Input work=\(\frac{\text{Output work}}{\text{Efficiency}}\)
For the eighteenth row: \(\frac{846}{0.167}\approx5066\)
For the nineteenth row: \(\frac{480}{0.547}\approx878\)

Answer:

Input Work (J)	Output Work (J)	Heat Lost (J)	Efficiency
321	147	174	0.458
746	465	281	0.623
998	360	638	0.361
725	126	599	0.174
782	364	418	0.465
429	30	399	0.070
820	118	702	0.144
525	184	341	0.350
964	742	222	0.770
1729	928	801	0.537
183	32	151	0.175
1449	841	608	0.580
1219	597	622	0.490
1890	989	901	0.523
303	34	269	0.111
480	305	175	0.635
5066	846	4220	0.167
878	480	398	0.547