# Estimate the mass of the water (Carnot cycle)

• fizzyfiz
In summary, the problem involves estimating the mass of water that can be heated from 20 to 100 degrees Celsius using a phone battery with a voltage of 3.6 and capacity of 2800 mAh through a backward Carnot cycle. The energy delivered by the battery is assumed to be transferred to the water, and the change in entropy of the water and surroundings needs to be taken into account. The solution can be expressed as a function of time, using the mass and heat capacity of the water.
fizzyfiz
Homework Statement
Given voltage and current, estimate how much mass of water can be heated from 20 to 100 degrees celsius by carnot heat pump. No heat losses. I came up with the idea of equation below, temperature is changing, so is efficiency. I sum multiples of heat required to increase tempreture by dT and efficiency at that T but I do not have any idea how to involve energy supplied into calculations.

I used "S" here to indicate integral.
Relevant Equations
Q=(293, 373)S T/T-293 *cm dT
m=Q/c(79*ln80)

fizzyfiz said:
Homework Statement: Given voltage and current, estimate how much mass of water can be heated from 20 to 100 degrees celsius by carnot heat pump. No heat losses. I came up with the idea of equation below, temperature is changing, so is efficiency. I sum multiples of heat required to increase tempreture by dT and efficiency at that T but I do not have any idea how to involve energy supplied into calculations.

I used "S" here to indicate integral.
Homework Equations: Q=(293, 373)S T/T-293 *cm dT

m=Q/c(79*ln80)
Please provide the exact word-for-word statement of the problem.

Estimate how much mass can be heated from 20( same as surroudnigs) to 100 degress celsius using phone battery of volatge 3.6 and capacity of 2800 mAh using heat pump. Heat pump must be treated as carnot cycle backwards.

So I know that the coefficient is changing as temperature is changing. The energy delivered to the water is sum of all coeficients multiplied by the energy to heat the mass of water by 1K. I am struggling to write the sum properly.

fizzyfiz said:
Estimate how much mass can be heated from 20( same as surroudnigs) to 100 degress celsius using phone battery of volatge 3.6 and capacity of 2800 mAh using heat pump. Heat pump must be treated as carnot cycle backwards.

So I know that the coefficient is changing as temperature is changing. The energy delivered to the water is sum of all coeficients multiplied by the energy to heat the mass of water by 1K. I am struggling to write the sum properly.
Do they give you any indication of how long the battery is delivering the power to run the heat pump?

Chestermiller said:
Do they give you any indication of how long the battery is delivering the power to run the heat pump?
No they do not. I think that I should assume that the whole energy is transfered.

fizzyfiz said:
No they do not. I think that I should assume that the whole energy is transfered.
To get the whole energy, you have to specify the amount of time the battery is delivering power. You can express the answer to this question as a function of t, the time of operation.

The energy delivered by the battery is equal to volatage*2800 mA*3600s *10^-3. Then it is trasfered to water via backward Carnot cycle.

fizzyfiz said:
The energy delivered by the battery is equal to volatage*2800 mA*3600s *10^-3. Then it is trasfered to water via backward Carnot cycle.
Where in your problem statement does it say anything about an hour?

They does not but I am given capacity of battery in mAh. So I multiply it by 3600 s to get charge in columbs.

fizzyfiz said:
They does not but I am given capacity of battery in mAh. So I multiply it by 3600 s to get charge in columbs.
Oh. OK. I missed that.

OK. Let M represent the mass of the water and C represent the heat capacity of the water. In terms of M and C, what is the change in entropy of the water in going from 20 C to 100 C? In terms of M and C, how much heat Q is added to the water in going from 20 C to 100 C?

If the heat pump is operated reversibly, what is the change in entropy of the surroundings (cold reservoir)?

I managed to do it by myself yesterday, thank you for your help :)

## 1. What is the Carnot cycle?

The Carnot cycle is a theoretical thermodynamic cycle that describes the most efficient way to convert heat into work. It consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

## 2. Why is it important to estimate the mass of water in the Carnot cycle?

Estimating the mass of water is important because it is a crucial component in the Carnot cycle. The mass of water affects the efficiency and performance of the cycle, as well as the amount of work that can be produced.

## 3. How do you calculate the mass of water in the Carnot cycle?

The mass of water in the Carnot cycle can be calculated by using the equation: m = Q / (h1-h2), where m is the mass of water, Q is the heat supplied to the system, and h1 and h2 are the enthalpies of the water at the beginning and end of the cycle, respectively.

## 4. What factors can affect the estimated mass of water in the Carnot cycle?

The estimated mass of water in the Carnot cycle can be affected by various factors such as the temperature and pressure of the water, the type of working fluid used, and any inefficiencies in the system. These factors can lead to variations in the actual mass of water used in the cycle.

## 5. How does the estimated mass of water impact the overall efficiency of the Carnot cycle?

The estimated mass of water has a direct impact on the efficiency of the Carnot cycle. A larger mass of water can result in a more efficient cycle, as it can absorb and release more heat, while a smaller mass of water may lead to lower efficiency due to less heat transfer. Therefore, accurately estimating the mass of water is crucial for optimizing the efficiency of the Carnot cycle.

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