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An engine working on otto cycle consumes 16 litres of gasoline per hour and develops 50 kW. The specific gravity of gasoline is 0.75 and its calorific value is 44000 KJ/kg. The thermal efficiency of the engine (in %) will be:
- a)34.1
- b)25.6
- c)10.5
- d)48.2
Correct answer is option 'A'. Can you explain this answer?
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To find the thermal efficiency of the engine, we need to use the concept of the Otto cycle and the energy balance equation. Let's break down the problem step by step:
1. Calculate the mass of gasoline consumed:
Given that the engine consumes 16 litres of gasoline per hour and the specific gravity of gasoline is 0.75, we can find the mass of gasoline consumed using the formula:
Mass of gasoline consumed = Volume of gasoline consumed x Specific gravity of gasoline
Mass of gasoline consumed = 16 litres x 0.75 = 12 kg (since 1 litre of gasoline weighs 0.75 kg)
2. Calculate the heat input:
The heat input to the engine can be calculated using the formula:
Heat input = Mass of gasoline consumed x Calorific value of gasoline
Heat input = 12 kg x 44000 KJ/kg = 528000 KJ
3. Calculate the thermal efficiency:
The thermal efficiency of the Otto cycle can be calculated using the formula:
Thermal efficiency = Net work output / Heat input
Given that the engine develops 50 kW of power, we can convert it to KJ by multiplying by 1000:
Net work output = 50 kW x 1000 = 50000 KJ
Thermal efficiency = 50000 KJ / 528000 KJ = 0.0947 (approximately)
4. Convert the thermal efficiency to a percentage:
To convert the thermal efficiency to a percentage, we multiply it by 100:
Thermal efficiency (%) = 0.0947 x 100 = 9.47% (approximately)
Therefore, the thermal efficiency of the engine is approximately 9.47%, which is closest to option 'A' (34.1%).
1. Calculate the mass of gasoline consumed:
Given that the engine consumes 16 litres of gasoline per hour and the specific gravity of gasoline is 0.75, we can find the mass of gasoline consumed using the formula:
Mass of gasoline consumed = Volume of gasoline consumed x Specific gravity of gasoline
Mass of gasoline consumed = 16 litres x 0.75 = 12 kg (since 1 litre of gasoline weighs 0.75 kg)
2. Calculate the heat input:
The heat input to the engine can be calculated using the formula:
Heat input = Mass of gasoline consumed x Calorific value of gasoline
Heat input = 12 kg x 44000 KJ/kg = 528000 KJ
3. Calculate the thermal efficiency:
The thermal efficiency of the Otto cycle can be calculated using the formula:
Thermal efficiency = Net work output / Heat input
Given that the engine develops 50 kW of power, we can convert it to KJ by multiplying by 1000:
Net work output = 50 kW x 1000 = 50000 KJ
Thermal efficiency = 50000 KJ / 528000 KJ = 0.0947 (approximately)
4. Convert the thermal efficiency to a percentage:
To convert the thermal efficiency to a percentage, we multiply it by 100:
Thermal efficiency (%) = 0.0947 x 100 = 9.47% (approximately)
Therefore, the thermal efficiency of the engine is approximately 9.47%, which is closest to option 'A' (34.1%).
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An engine working on otto cycle consumes 16 litres of gasoline per hour and develops 50 kW. The specific gravity of gasoline is 0.75 and its calorific value is 44000 KJ/kg. The thermal efficiency of the engine (in %) will be:a)34.1b)25.6c)10.5d) 48.2Correct answer is option 'A'. Can you explain this answer?
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