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A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.
Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgK
Correct answer is '60'. Can you explain this answer?
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A perfect reversed heat engine is used for making ice at -5°C from wa...
Given T1= 298 K and T2 = 263 K
A perfect reversed heat engine works on Carnot cycle for which COP in terms of temperatures is given by
COP = T2/(T1 - T2) = 263/(298-263) = 7.514
Work input = 1 kWhr = 3600 kJ
In terms of heat and work interactions,
COP = Q2/(Q1 - Q2) = Q2/W
⇒ Q2 = W X COP
= 3600 x 7.514
= 27050 kJ/hr
Q2 = Total heat extracted from ice
Removal of heat from 1 kg of water at 25°C
So that it becomes at -5°C is given by
= mCpWΔT + mL + mCpΔT
= 1 x 4.18 x (25 - 0) + 1 x 335 + 1 x 2.1[0 -(-5)]
= 450.15 kJ
∴ Ice formed per kWhr = 27050/450.15 = 60.09 kg
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A perfect reversed heat engine is used for making ice at -5°C from wa...
To solve this problem, we need to consider the concept of a reversed heat engine and the energy required to form ice from water.
1. Reversed Heat Engine:
A reversed heat engine operates in reverse of a typical heat engine. Instead of converting thermal energy into mechanical work, it converts mechanical work into thermal energy. In this case, the reversed heat engine is used to extract heat from the water and lower its temperature to -5°C.
2. Energy required to form ice:
To form ice, we need to extract heat from the water and lower its temperature to the freezing point of water, which is 0°C. Then, we need to extract additional heat to convert the water at 0°C to ice at 0°C. The energy required can be calculated using the specific heat and latent heat of ice.
The energy required to lower the temperature of water from 25°C to 0°C can be calculated as:
Q1 = mass of water * specific heat of water * (final temperature - initial temperature)
Q1 = mass of water * 4.18 kJ/kgK * (0°C - 25°C)
The energy required to convert the water at 0°C to ice at 0°C can be calculated as:
Q2 = mass of water * latent heat of ice
3. Calculation:
Now, let's calculate the mass of water using the energy input of 1 kWhr (3600 kJ). We can assume that the reversed heat engine is 100% efficient, meaning all the mechanical work input is converted into thermal energy.
The energy input to the reversed heat engine is 3600 kJ. Since the engine is 100% efficient, this energy is equal to the energy required to form ice, which is Q1 + Q2.
3600 kJ = mass of water * 4.18 kJ/kgK * (0°C - 25°C) + mass of water * latent heat of ice
Simplifying this equation, we get:
3600 kJ = mass of water * (-104.5 kJ/kg) + mass of water * 335 kJ/kg
Rearranging the equation to solve for mass of water, we get:
mass of water = 3600 kJ / (335 kJ/kg - 104.5 kJ/kg)
Calculating this, we find that the mass of water is approximately 60 kg.
4. Quantity of ice formed per kWhr:
Since the density of ice is the same as water, the mass of ice formed is also 60 kg.
Therefore, the quantity of ice formed per kWhr is 60 kg.
1. Reversed Heat Engine:
A reversed heat engine operates in reverse of a typical heat engine. Instead of converting thermal energy into mechanical work, it converts mechanical work into thermal energy. In this case, the reversed heat engine is used to extract heat from the water and lower its temperature to -5°C.
2. Energy required to form ice:
To form ice, we need to extract heat from the water and lower its temperature to the freezing point of water, which is 0°C. Then, we need to extract additional heat to convert the water at 0°C to ice at 0°C. The energy required can be calculated using the specific heat and latent heat of ice.
The energy required to lower the temperature of water from 25°C to 0°C can be calculated as:
Q1 = mass of water * specific heat of water * (final temperature - initial temperature)
Q1 = mass of water * 4.18 kJ/kgK * (0°C - 25°C)
The energy required to convert the water at 0°C to ice at 0°C can be calculated as:
Q2 = mass of water * latent heat of ice
3. Calculation:
Now, let's calculate the mass of water using the energy input of 1 kWhr (3600 kJ). We can assume that the reversed heat engine is 100% efficient, meaning all the mechanical work input is converted into thermal energy.
The energy input to the reversed heat engine is 3600 kJ. Since the engine is 100% efficient, this energy is equal to the energy required to form ice, which is Q1 + Q2.
3600 kJ = mass of water * 4.18 kJ/kgK * (0°C - 25°C) + mass of water * latent heat of ice
Simplifying this equation, we get:
3600 kJ = mass of water * (-104.5 kJ/kg) + mass of water * 335 kJ/kg
Rearranging the equation to solve for mass of water, we get:
mass of water = 3600 kJ / (335 kJ/kg - 104.5 kJ/kg)
Calculating this, we find that the mass of water is approximately 60 kg.
4. Quantity of ice formed per kWhr:
Since the density of ice is the same as water, the mass of ice formed is also 60 kg.
Therefore, the quantity of ice formed per kWhr is 60 kg.
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A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer?
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A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer?.
A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A perfect reversed heat engine is used for making ice at -5°C from water available at 25°C. The temperature of freezing mixture is -10°C. The quantity of ice formed (in kg) per kWhr is___________.Take specific heat of ice as 2.1 kJ/kgK and latent heat of ice as 335 kJ /kg. Cpw = 4.18 kJ/kgKCorrect answer is '60'. Can you explain this answer?.
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