An air-standard Diesel cycle engine operates as follows: The temperatures at the beginning and end of the compression stroke are 30 °C and 700 °C, respectively. The net work per cycle is 590.1 kJ/kg, and the heat transfer input per cycle is 925 kJ/kg. Determine the a) compression ratio, b) maximum temperature of the cycle, and c) the cutoff ratio, v3/v2.

This question is incomplete, the complete question is;

An air-standard Diesel cycle engine operates as follows: The temperatures at the beginning and end of the compression stroke are 30 °C and 700 °C, respectively. The net work per cycle is 590.1 kJ/kg, and the heat transfer input per cycle is 925 kJ/kg. Determine the a) compression ratio, b) maximum temperature of the cycle, and c) the cutoff ratio, v3/v2.

Use the cold air standard assumptions.

Answer:

a) The compression ratio is 18.48

b) The maximum temperature of the cycle is 1893.4 K

c) The cutoff ratio, v₃/v₂ is 1.946

Explanation:

Given the data in the question;

Temperature at the start of a compression T₁ = 30°C = (30 + 273) = 303 K

Temperature at the end of a compression T₂ = 700°C = (700 + 273) = 973 K

Net work per cycle [tex]W_{net[/tex] = 590.1 kJ/kg

Heat transfer input per cycle Qs = 925 kJ/kg

a) compression ratio;

As illustrated in the diagram below, 1 - 2 is adiabatic compression;

so,

Tγ[tex]^{Y-1[/tex] = constant { For Air, γ = 1.4 }

hence;

⇒ V₁ / V₂ = [tex]([/tex] T₂ / T₁ [tex])^{\frac{1}{Y-1}[/tex]

so we substitute

⇒ V₁ / V₂ = [tex]([/tex]  973 K / 303 K  [tex])^{\frac{1}{1.4-1}[/tex]

= [tex]([/tex]  3.21122  [tex])^{\frac{1}{0.4}[/tex]

= 18.4788 ≈ 18.48

Therefore, The compression ratio is 18.48

b) maximum temperature of the cycle

We know that for Air, Cp = 1.005 kJ/kgK

Now,

Heat transfer input per cycle Qs = Cp( T₃ - T₂ )

we substitute

925 = 1.005( T₃ - 700 )

( T₃ - 700 ) = 925 / 1.005

( T₃ - 700 ) = 920.398

T₃ = 920.398 + 700

T₃ = 1620.398 °C

T₃ = ( 1620.398 + 273 ) K

T₃ = 1893.396 K ≈ 1893.4 K

Therefore, The maximum temperature of the cycle is 1893.4 K

c)  the cutoff ratio, v₃/v₂;

Since pressure is constant, V ∝ T

So,

cutoff ratio S = v₃ / v₂  = T₃ / T₂

we substitute

cutoff ratio S = 1893.396 K / 973 K

cutoff ratio S = 1.9459 ≈ 1.946

Therefore, the cutoff ratio, v₃/v₂ is 1.946

QUESTION 1
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Case Study # 1: Cadbury Crisis Management (Worm Controversy)

In India chocolate consumption was very low in the early 90’s but as the decade advanced the consumption drastically increased. The late 90’s witnessed a good chocolate market condition. The chocolate market in India is dominated by two multinational companies – Cadbury and Nestle. The national companies – Amul and Campco are other candidates in this race. Cadbury holds more than 70% of the total share of the market. Nestle has emerged by holding almost 20% of the total share. Apart from chocolate segment, there is also a big confectionery segment which is flooded by companies like Parry’s, Ravalgaon, Candico and Nutrine. All these are leading national players. The multinational companies like the Cadbury, Nestle and Perfetti are the new entrants in the sugar confectionery market. (Management paradise) There are several others which have a minor share in these two segments. According to statistics, the chocolate consumption in India is extremely low. If per capita consumption is considered, it comes to only 160gms in the urban areas. This amount is very low compared to the developed countries where the per capita consumption is more than 8-10kg. Observing this fact it would not be appropriate to consider the rural areas of India as it will be extremely low. This low consumption is owing to the notion behind consuming chocolates. Indians eat chocolates as indulgence and not as snack food. The major target population is the children. India has witnessed a slow growth rate of about 10% pa from the 70’s to the 80’s. But as the century advanced the market stagnated. This was the time when Cadbury launched its product- Dairy Milk as an anytime product rather than an occasional luxury. All the advertisements of Dairy Milk paid a full attention to adults and not children. And this proved to be the major breakthrough for Cadbury as it tried to break the conventional ideas of the Indians about chocolate.

The Worm Controversy
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