# Specific heat capacity of the final temp

• DDV805
In summary, the conversation is about a problem involving an experimental material cup that can hold hot liquids without increasing its own temperature. The cup, which weighs .79 kg and has an initial temperature of 37.9 C, is submerged in 1.17 kg of water with an initial temperature of 21.8 C. The goal is to find the cup's specific heat capacity, assuming the system is closed and using the given data to calculate the energy transferred between the cup and water.
DDV805
Hi, could someone help me get started on this problem, I am having a lot of difficulty comprehending these types of problems. THanks for your help guys.

A cup is made of an experimental material that can hold hot liquids without significantly increasing its own temperature. THe .79 kg cup has an initial temperature of 37.9 C when it is submerged in 1.17 kg of water with an initial temperature of 21.8 C.
What is the cups specific heat capacity if the final temperature is 24.2 C.

To get you started:

1. Think about which way does the heat flow between the cup and water, why there is energy transfer and at what condition there is equilibrium.
2. Assume the system is closed
3. From the given data you can calculate the energy tranferred between the components of the system. From that you can solve for the cups specific heat cap.

Sure, I can help you get started on this problem. First, let's define what specific heat capacity is. Specific heat capacity is the amount of heat energy required to raise the temperature of one unit of mass by one degree Celsius. In this case, we are trying to find the specific heat capacity of the cup, which is a measure of how much heat energy is needed to raise the temperature of the cup by one degree Celsius.

To solve this problem, we can use the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. We know the mass of the cup is 0.79 kg and the change in temperature is 37.9 C - 24.2 C = 13.7 C. We also know that the cup is not significantly increasing in temperature, so we can assume that its specific heat capacity is very high.

Now, we need to find the heat energy (Q) for the cup. We can do this by using the same formula, but this time we need to use the mass and temperature of the water. The mass of the water is 1.17 kg and the change in temperature is 24.2 C - 21.8 C = 2.4 C. So, the heat energy for the water is Q = (1.17 kg)(4.186 J/gC)(2.4 C) = 9.86 J.

Now, we can substitute the values we know into the original formula and solve for the specific heat capacity of the cup. 9.86 J = (0.79 kg)(c)(13.7 C). Solving for c, we get c = 0.94 J/gC. This means that it takes 0.94 joules of energy to raise the temperature of 1 gram of the cup by 1 degree Celsius.

I hope this helps you understand the problem better and get started on solving it. Remember to always double check your units and make sure they cancel out to give you the correct units for the final answer. Good luck!

## What is specific heat capacity?

Specific heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius or Kelvin. It is measured in Joules per gram per degree Celsius (J/g°C) or in Joules per mole per Kelvin (J/mol*K).

## How is specific heat capacity calculated?

Specific heat capacity can be calculated by dividing the amount of heat transferred by the change in temperature and the mass of the substance. It can also be determined by using the equation q = mcΔT, where q is the amount of heat, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.

## Why is specific heat capacity important?

Specific heat capacity is important because it helps us understand how much energy is needed to change the temperature of a substance. It also plays a crucial role in many scientific fields, including thermodynamics, chemistry, and engineering.

## How does specific heat capacity affect the final temperature of a substance?

The specific heat capacity of a substance determines how much energy is required to raise its temperature. Therefore, the higher the specific heat capacity, the more energy is needed to change the temperature and the longer it will take to reach a final temperature.

## What factors can affect the specific heat capacity of a substance?

The specific heat capacity of a substance can be affected by its molecular structure, phase (solid, liquid, gas), and temperature. It can also be influenced by the presence of impurities or other substances in the mixture.

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