# How Does Mixing Coffee, Cream, and a Ceramic Cup Affect Temperature Equilibrium?

• map7s
In summary, the conversation discusses the use of the specific heat equation (c=Q/(mdeltaT)) to calculate the equilibrium temperature of a ceramic coffee cup, initially at room temperature, after adding 80.3°C coffee and 5.00°C cream. The equation is used to relate the increase in energy (Q) to the decrease in energy (mdeltaT), but the value for Q cannot be calculated without more information.
map7s
A ceramic coffee cup, with m = 137 g and c = 1090 J/(kgK), is initially at room temperature (24.0°C). If 265 g of 80.3°C coffee and 12.2 g of 5.00°C cream are added to the cup, what is the equilibrium temperature of the system? Assume that no heat is exchanged with the surroundings, and that the specific heat of coffee and cream are the same as the specific heat of water.

I tried to use the equation c=Q/(mdeltaT) but I'm not sure what to plug in for Q because I can't calculate its value. Am I completely off track about the equation?

Ummm... Sort of. Try writing out the whole equation that relates increase in energy and decrease in energy.

No, you are on the right track with using the equation c=Q/(mdeltaT). In this scenario, Q represents the amount of heat energy transferred to the system. Since we are assuming that no heat is exchanged with the surroundings, the total amount of heat energy in the system will remain constant. Therefore, we can set the heat gained by the coffee and cream equal to the heat lost by the ceramic cup.

We can calculate the heat gained by the coffee using the equation Q=mc(deltaT), where m is the mass of the coffee (265 g) and c is the specific heat of water (4.18 J/(gK)). We can also calculate the heat gained by the cream using the same equation, but with the mass and initial temperature of the cream (12.2 g and 5.00°C).

Now, we can set the sum of these two heat gains equal to the heat lost by the ceramic cup. We can calculate the heat lost by the cup using the same equation, but with the mass and initial temperature of the cup (137 g and 24.0°C).

Once we have set these two equations equal to each other, we can solve for the equilibrium temperature (deltaT). This will give us the final temperature at which the system will reach equilibrium.

Using this approach, we can calculate the equilibrium temperature to be approximately 78.3°C. This means that the final temperature of the system after adding the coffee and cream will be 78.3°C.

It is also important to note that we are assuming that the specific heat of the coffee and cream are the same as water. This may not be entirely accurate, but it is a reasonable approximation. Additionally, if we take into account the slight differences in specific heat, the equilibrium temperature may vary slightly from the calculated value. However, this approach will give us a good estimate of the final temperature of the system.

## Q: What causes changes in temperatures?

Changes in temperatures are primarily caused by natural processes such as the Earth's tilt and orbit, as well as human activities such as burning fossil fuels and deforestation. These processes can lead to an increase or decrease in the amount of heat trapped in the Earth's atmosphere, resulting in changes in temperatures.

## Q: How do scientists measure changes in temperatures?

Scientists use a variety of methods to measure changes in temperatures, such as weather stations, satellites, and ocean buoys. These tools gather data on temperature readings from different locations and can track changes over time to determine patterns and trends.

## Q: Are changes in temperatures the same all over the world?

No, changes in temperatures can vary greatly depending on location. Some areas may experience more drastic changes due to factors such as proximity to oceans, elevation, and land use. It's important for scientists to study changes in temperatures globally to understand the overall impact on the Earth's climate.

## Q: How do changes in temperatures affect the environment?

Changes in temperatures can have a significant impact on the environment. It can lead to changes in rainfall patterns, melting of ice caps and glaciers, and shifts in ecosystems. These changes can have consequences on wildlife, agriculture, and human populations.

## Q: Can changes in temperatures be reversed?

While some changes in temperatures may be reversed through natural processes, such as a decrease in greenhouse gas emissions, others may have long-lasting effects. It's important for individuals and governments to take action to reduce the negative impacts of changes in temperatures and to work towards sustainable solutions.

• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
9
Views
6K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
13
Views
4K
• Introductory Physics Homework Help
Replies
4
Views
6K
• Introductory Physics Homework Help
Replies
1
Views
954
• Biology and Chemistry Homework Help
Replies
3
Views
4K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
9
Views
3K