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The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is:- (a) 26.8% (b) 20% (c) 6.25% (d) 12.5%?
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Calculation of Efficiency of an Ideal Heat Engine
To calculate the efficiency of an ideal heat engine, we need to use the Carnot cycle. The Carnot cycle is the most efficient cycle that a heat engine can operate on.
The Carnot cycle consists of four processes:
1. Isothermal Expansion: In this process, the working substance (gas) is heated at a constant temperature (T1) and expands.
2. Adiabatic Expansion: In this process, the working substance expands without any heat being added or removed.
3. Isothermal Compression: In this process, the working substance is compressed at a constant temperature (T2) and heat is removed.
4. Adiabatic Compression: In this process, the working substance is compressed without any heat being added or removed.
The efficiency of an ideal heat engine can be calculated using the following formula:
Efficiency = 1 - (T2/T1)
where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.
Calculation of Efficiency between Freezing and Boiling Point of Water
The freezing point of water is 0°C and the boiling point of water is 100°C. Therefore, the temperature difference (T1-T2) between the hot and cold reservoirs is 100°C.
Using the formula for efficiency, we can calculate the efficiency of an ideal heat engine operating between the freezing and boiling points of water:
Efficiency = 1 - (T2/T1) = 1 - (273/373) = 1 - 0.731 = 0.269 or 26.9%
Therefore, the efficiency of an ideal heat engine operating between the freezing and boiling points of water is 26.9% or approximately 26.8% (rounded to one decimal place).
Answer: (a) 26.8%
To calculate the efficiency of an ideal heat engine, we need to use the Carnot cycle. The Carnot cycle is the most efficient cycle that a heat engine can operate on.
The Carnot cycle consists of four processes:
1. Isothermal Expansion: In this process, the working substance (gas) is heated at a constant temperature (T1) and expands.
2. Adiabatic Expansion: In this process, the working substance expands without any heat being added or removed.
3. Isothermal Compression: In this process, the working substance is compressed at a constant temperature (T2) and heat is removed.
4. Adiabatic Compression: In this process, the working substance is compressed without any heat being added or removed.
The efficiency of an ideal heat engine can be calculated using the following formula:
Efficiency = 1 - (T2/T1)
where T1 is the temperature of the hot reservoir and T2 is the temperature of the cold reservoir.
Calculation of Efficiency between Freezing and Boiling Point of Water
The freezing point of water is 0°C and the boiling point of water is 100°C. Therefore, the temperature difference (T1-T2) between the hot and cold reservoirs is 100°C.
Using the formula for efficiency, we can calculate the efficiency of an ideal heat engine operating between the freezing and boiling points of water:
Efficiency = 1 - (T2/T1) = 1 - (273/373) = 1 - 0.731 = 0.269 or 26.9%
Therefore, the efficiency of an ideal heat engine operating between the freezing and boiling points of water is 26.9% or approximately 26.8% (rounded to one decimal place).
Answer: (a) 26.8%
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The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is:- (a) 26.8% (b) 20% (c) 6.25% (d) 12.5%?
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