# Deriving Specific Heat Equations

• jasmine689
In summary, the conversation is about deriving two equations, one for c and one for L, in a given system involving water, a calorimeter, and ice. The equations involve various variables such as mass, temperature, and specific heat. The person seeking help is struggling to receive assistance and is asking for any sort of attempt or guidance before a deadline of 3pm.
jasmine689

## Homework Statement

Derive the Following Equations:
c = [(m_w*c_w + m_c*c_al) (T_e - T_i)] / m_s*(T_s - T_e)
and
L = (m_w*c_w + m_c*c_al) * (T_i - T_e) - m_I*c_w * [(T_e- T_m)/m_I]

## Homework Equations

T_i - initial temp of water and calorimeter
T_m - melting temp of ice
T_e - equilibrium temp of system
m_w- mass of water
m_c - mass of calorimeter
m_I - mass of ice
c_w - specific heat of water
c_al - specifical heat of aluminum
L - unknown heat of fusion

## The Attempt at a Solution

...trying to receive help from my teacher's assistant, but not being able to do so :[

Any attempts at either equations, wrong or right, will be fully appreciated.

PLEASE ANY kind of help, even if it's not completed, would be REALLY appreciated :)

...I need this done in by 3pm today...

The specific heat equation is a fundamental equation used in thermodynamics to calculate the amount of heat energy needed to raise the temperature of a substance. It is derived from the first law of thermodynamics, which states that energy cannot be created or destroyed, only transferred from one form to another.

To derive the first equation, we can start by considering the heat energy transferred from the water and calorimeter to the system, which is equal to the heat energy gained by the system. This can be written as:

Q = (m_w * c_w + m_c * c_al) * (T_e - T_i)

Where Q is the heat energy, m_w and m_c are the masses of water and calorimeter, c_w and c_al are the specific heats of water and aluminum, and T_e and T_i are the initial and equilibrium temperatures of the system.

Next, we can consider the heat energy lost by the system due to the change in temperature of the system (from T_s to T_e). This can be written as:

Q = m_s * c_s * (T_s - T_e)

Where m_s is the mass of the system and c_s is its specific heat.

Equating these two equations, we get:

(m_w * c_w + m_c * c_al) * (T_e - T_i) = m_s * c_s * (T_s - T_e)

Solving for c_s, we get:

c_s = [(m_w * c_w + m_c * c_al) * (T_e - T_i)] / (m_s * (T_s - T_e))

This is the first equation that we were asked to derive.

To derive the second equation, we can use the same approach. We can consider the heat energy gained by the water and calorimeter, which is equal to the heat energy lost by the ice and system. This can be written as:

Q = (m_w * c_w + m_c * c_al) * (T_i - T_e) + m_I * c_w * (T_e - T_m)

Where m_I is the mass of ice and T_m is the melting temperature of ice.

Next, we can consider the heat energy gained by the system due to the heat of fusion (L) of the ice. This can be written as:

Q = m_I * L

Equating these two equations, we get:

(m_w * c_w + m_c *

## 1. What is specific heat and why is it important in scientific calculations?

Specific heat is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius. It is important in scientific calculations because it helps determine the amount of energy needed to change the temperature of a substance, and it can also be used to identify unknown substances.

## 2. How do you derive the specific heat equation?

The specific heat equation can be derived by rearranging the equation for heat transfer, Q = mcΔT, where Q is the amount of heat transferred, m is the mass of the substance, c is the specific heat, and ΔT is the change in temperature.

## 3. What are the different types of specific heat equations?

The most common types of specific heat equations are the specific heat capacity equation, which calculates the specific heat at a constant pressure, and the specific heat volume equation, which calculates the specific heat at a constant volume.

## 4. Can the specific heat of a substance change?

Yes, the specific heat of a substance can change depending on the temperature and pressure conditions. In some cases, it can also vary with the composition of the substance.

## 5. How is the specific heat of a substance measured experimentally?

The specific heat of a substance can be measured experimentally by using a calorimeter, which measures the heat transferred between a substance and its surroundings. The specific heat can then be calculated using the mass of the substance, the change in temperature, and the amount of heat transferred.

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