# Solving Heat Engine Problem: Power Output Calculation

• abro369
In summary, a heat engine is operating with a hot reservoir at 100 degrees Celsius (373 Kelvin) and a cold reservoir at 0 degrees Celsius (273 Kelvin). In 1.3 seconds, 12 grams of steam condenses and 59 grams of ice melts. The power output of the heat engine can be calculated using the equation W=Q_h - Q_c, where n=W/Q_h=1 - (T_c/T_h). The units for the given numbers are not specified, but it is important to note that the temperatures are in degrees Celsius (or Kelvin). The amounts of steam and ice are in grams. Using the given information, one can solve for the thermal coefficient and then use it to find the power output
abro369

## Homework Statement

The hot reservoir of a heat engine is steam at 100 while the cold reservoir is ice at 0. In 1.3 of operation, 12 of steam condenses and 59 of ice melts.
What is the power output of the heat engine?

## Homework Equations

W=Q_h - Q_c
n=W/Q_h=1 - (T_c/T_h)
Q=ML

## The Attempt at a Solution

All I could think to do was solve for the thermal coefficient.
n=1-(273/373)

I'm not sure where to go from here.

abro369 said:

## Homework Statement

The hot reservoir of a heat engine is steam at 100 while the cold reservoir is ice at 0. In 1.3 of operation, 12 of steam condenses and 59 of ice melts.
What is the power output of the heat engine?
Please tell us what units go with these numbers!
Okay, it's fairly obvious the temperatures are in degrees Celsius, but you do need to tell us what units go with the 1.3, 12, and 59.

Hint: the condensing and melting info is useful for finding Qh and Qc.

I would first clarify the problem and make sure that all the necessary information is provided. It is important to know the specific heat capacity of steam and ice, as well as the time frame for the operation of the heat engine. Additionally, it would be helpful to know the efficiency of the heat engine, as this would affect the power output calculation.

Assuming we have all the necessary information, we can proceed with the solution. The first step would be to calculate the amount of heat absorbed by the hot reservoir (Q_h) and the amount of heat released by the cold reservoir (Q_c). This can be done using the formula Q=ML, where M is the mass and L is the specific heat capacity.

Q_h = 12 kg * L_steam * (100°C - 0°C)
Q_h = 1200 L_steam

Q_c = 59 kg * L_ice * (0°C - 0°C)
Q_c = 0

Next, we can calculate the work done by the heat engine using the formula W=Q_h - Q_c.

W = 1200 L_steam - 0
W = 1200 L_steam

Finally, we can calculate the power output of the heat engine by dividing the work done by the time of operation.

Power output = W / time
Power output = 1200 L_steam / 1.3 hours
Power output = 923.08 L_steam/hour

However, it is important to note that this is just a rough estimate as we do not have all the necessary information. To get a more accurate calculation, we would need to know the efficiency of the heat engine and the specific heat capacities of steam and ice.

## What is a heat engine and how does it work?

A heat engine is a device that converts thermal energy into mechanical energy. It operates by using a heat source, such as burning fuel, to produce heat and then using that heat to do work. The work produced is typically in the form of rotating a shaft, which can then be used to power machinery.

## What are the main components of a heat engine?

The main components of a heat engine are the heat source, the working fluid, the heat sink, and the mechanical system. The heat source provides the thermal energy, the working fluid absorbs and transfers the heat, the heat sink dissipates the excess heat, and the mechanical system converts the thermal energy into mechanical work.

## How do you calculate the power output of a heat engine?

The power output of a heat engine can be calculated using the formula P = Q/t, where P is power, Q is the heat energy transferred, and t is the time it takes for the heat energy to be transferred. This formula assumes that the heat engine is operating at a steady state and that there are no energy losses.

## What factors affect the power output of a heat engine?

The power output of a heat engine is affected by several factors, including the efficiency of the engine, the temperature difference between the heat source and the heat sink, and the type of working fluid used. Additionally, any energy losses due to friction or other inefficiencies will also impact the power output.

## How can the power output of a heat engine be increased?

The power output of a heat engine can be increased by improving its efficiency, using a higher temperature heat source, and/or reducing the temperature of the heat sink. Additionally, using a more efficient working fluid and reducing energy losses can also lead to an increase in power output.

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