Thermodynamics - Manipulating differentials

In summary, thermodynamics is the branch of science that studies the relationship between heat and energy. Manipulating differentials in thermodynamics refers to controlling small changes in thermodynamic variables to achieve a desired outcome, such as changing the temperature or pressure of a system. This process is related to the first law of thermodynamics, which states that energy cannot be created or destroyed, only transformed. Manipulating differentials has practical applications in areas such as refrigeration, power plants, and chemical processing, where precise control over thermodynamic variables is necessary.
  • #1
Gashoe13
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Homework Statement


We're told to show the attached equation, (partial P/partial V) at constant S = that big mess.

Homework Equations


dE=TdS - PdV

The Attempt at a Solution


lol just went in circles with the commuter and permuted rules. I have no clue how to end up where I'm supposed to be.
 

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  • #2
Try expressing E as E(V,P) and evaluating the differential of E in terms of partials with respect to V and P.
 
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1. What is thermodynamics?

Thermodynamics is the branch of science that deals with the relationship between heat and other forms of energy, such as work and internal energy. It studies how energy is transferred and transformed between different forms and how it affects the properties of matter.

2. What is meant by manipulating differentials in thermodynamics?

Manipulating differentials in thermodynamics refers to the process of changing or controlling the small changes in thermodynamic variables, such as temperature, pressure, and volume, in order to achieve a desired outcome or state of a system.

3. What are some examples of manipulating differentials in thermodynamics?

Some examples of manipulating differentials in thermodynamics include changing the temperature of a gas inside a cylinder by compressing or expanding it, adjusting the pressure and volume of a gas in a container to achieve a specific state, and altering the energy input or output of a system to achieve a desired change in temperature.

4. How is the first law of thermodynamics related to manipulating differentials?

The first law of thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. Manipulating differentials in thermodynamics involves changing the energy of a system by controlling the transfer of heat and work, which is in accordance with the first law.

5. What are the practical applications of manipulating differentials in thermodynamics?

Manipulating differentials in thermodynamics has many practical applications, such as in refrigeration and air conditioning systems, power plants, and engines. It also plays a crucial role in industries such as chemical and food processing, where precise control over temperature, pressure, and other thermodynamic variables is necessary for efficient and safe operation.

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