# Specific Heats for Incompressible Fluids

• Spectre5
If it is not provided, you can determine it experimentally by measuring the amount of heat required to change the temperature of the fluid by a certain amount. In summary, the equation Cp = Cv + R applies to compressible fluids, but for incompressible fluids, Cp = Cv since R is zero. However, the specific heat for an incompressible fluid can be determined experimentally.
Spectre5
Given the following equation:

Cp = Cv + R

Where Cp is specific heat (constant pressure), Cv is specific heat (constant volume), and R is the universal gas constant.

However, my book states that for an incompressible fluid, Cp = Cv.

How can this be the case given the above equation? R is a constant for any given fluid, so why is is zero for an incompressible fluid?

Nevermind, I think I figured it out

Can you explain to me what you figured out then (or someone)?
I don't understand how the specific heat for an ICL is supposed to be determined.

Elbobo said:
Can you explain to me what you figured out then (or someone)?
I don't understand how the specific heat for an ICL is supposed to be determined.
The specific heat is usually provided for you in the problem statement, or in a table somewhere in the textbook.

The equation Cp = Cv + R is a general equation that applies to all fluids, both compressible and incompressible. However, for incompressible fluids, the value of R is very small and can be considered negligible. This is because incompressible fluids do not exhibit significant changes in volume in response to changes in pressure, so the effect of R on the specific heat is minimal. Therefore, for practical purposes, the values of Cp and Cv for incompressible fluids can be considered equal. However, it is important to note that this is an approximation and may not hold true for all incompressible fluids under all conditions. Further research and experimentation may be needed to accurately determine the specific heats of incompressible fluids.

## 1. What is specific heat for incompressible fluids?

Specific heat for incompressible fluids is a measure of the amount of heat energy required to raise the temperature of a unit mass of the fluid by one degree. It is a thermodynamic property that is unique to each fluid and depends on factors such as the composition and temperature of the fluid.

## 2. How is specific heat for incompressible fluids measured?

The specific heat for incompressible fluids is typically measured using a calorimeter, which is a device that measures the heat transfer between a fluid and its surroundings. The fluid is heated or cooled and the change in temperature is recorded. The amount of heat added or removed and the change in temperature are then used to calculate the specific heat of the fluid.

## 3. What are the units for specific heat for incompressible fluids?

The units for specific heat for incompressible fluids are typically joules per kilogram per Kelvin (J/kg·K) in the SI system or calories per gram per degree Celsius (cal/g·°C) in the CGS system. These units represent the amount of heat energy required to raise the temperature of a unit mass of the fluid by one degree.

## 4. How does specific heat for incompressible fluids affect heat transfer?

The specific heat for incompressible fluids plays a crucial role in heat transfer processes. It determines the amount of heat energy that is required to raise the temperature of the fluid, and therefore, affects the rate of heat transfer. Fluids with higher specific heats require more energy to change their temperature, resulting in slower heat transfer rates.

## 5. What factors can affect the specific heat of incompressible fluids?

The specific heat of incompressible fluids can be affected by various factors such as temperature, pressure, and composition of the fluid. At different temperatures and pressures, the specific heat of a fluid may vary. Additionally, the specific heat can also be affected by the presence of impurities or dissolved substances in the fluid.

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