what is the capacity to do work and transfer heat?

Thermodynamics is a branch of physics which deals with the energy and work of a system. Thermodynamics deals only with the big scale response of a system which nosotros can observe and mensurate in experiments. In aerodynamics, we are most interested in thermodynamics for the role it plays in engine design and high speed flying.

On this slide we derive some equations which chronicle the rut capacity of a gas to the gas constant used in the equation of state. We are going to exist using specific values of the state variables. For a scientist, a "specific" state variable means the value of the variable divided by the mass of the substance. This allows us to derive relations between variables without regard for the amount of the substance that we have. We can multiply the specific variable by the quantity of the substance at any time to determine the bodily value of the catamenia variable. From our studies of heat transfer, we know that the amount of heat transferred between two objects is proportional to the temperature difference between the objects and the oestrus capacity of the objects. The heat capacity is a constant that tells how much heat is added per unit temperature rise. The value of the constant is dissimilar for different materials and depends on the process. Heat capacity is non a state variable.

If we are dealing with a gas, it is well-nigh user-friendly to utilize forms of the thermodynamics equations based on the enthalpy of the gas. From the definition of enthalpy:

h = e + p * v

where h in the specific enthalpy, p is the pressure, v is the specific volume, and e is the specific internal energy. During a procedure, the values of these variables change. Permit'southward denote the alter by the Greek alphabetic character delta which looks like a triangle. So "delta h" means the alter of "h" from state 1 to land ii during a process. Then, for a constant pressure level process the enthalpy equation becomes:

delta h = delta e + p * delta five

The enthalpy, internal energy, and book are all changed, but the pressure remains the aforementioned. From our derivation of the enthalpy equation, the change of specific enthalpy is equal to the heat transfer for a abiding pressure procedure:

delta h = cp * delta T

where delta T is the change of temperature of the gas during the process,and c is the specific heat capacity. Nosotros accept added a subscript "p" to the specific heat capacity to remind us that this value only applies to a constant pressure level process.

The equation of state of a gas relates the temperature, pressure level, and book through a gas abiding R . The gas abiding used by aerodynamicists is derived from the universal gas constant, merely has a unique value for every gas.

p * v = R * T

If we have a constant pressure process, then:

p * delta v = R * delta T

Now let united states imagine that we have a constant volume process with our gas that produces exactly the same temperature change as the constant force per unit area process that we have been discussing. Then the showtime law of thermodynamics tells us:

delta e = delta q - delta w

where q is the specific heat transfer and w is the piece of work done by the gas. For a constant volume procedure, the work is equal to zero. And we tin can express the estrus transfer as a abiding times the change in temperature. This gives:

delta e = cv * delta T

where delta T is the modify of temperature of the gas during the process,and c is the specific heat capacity. Nosotros have added a subscript "v" to the specific heat capacity to remind us that this value only applies to a abiding volume process. Even though the temperature change is the same for this procedure and the constant pressure level process, the value of the specific heat chapters is different.

Considering we have selected the constant volume process to requite the same change in temperature as our constant pressure procedure, we can substitute the expression given above for "delta e" into the enthalpy equation. In general, you tin't brand this substitution because a constant pressure level process and a constant book process produce different changes in temperature If we substitute the expressions for "delta eastward", "p * delta 5", and "delta h" into the enthalpy equation nosotros obtain:

cp * delta T = cv * delta T + R * delta T

dividing by "delta T" gives the relation:

cp = cv + R

The specific oestrus constants for constant pressure and abiding book processes are related to the gas constant for a given gas. This rather remarkable result has been derived from thermodynamic relations, which are based on observations of physical systems and processes. Using the kinetic theory of gases, this same result tin can be derived from considerations of the conservation of energy at a molecular level.

Nosotros can define an additional variable called the specific heat ratio, which is given the Greek symbol "gamma", which is equal to cp divided past cv:

gamma = cp / cv

"Gamma" is only a number whose value depends on the state of the gas. For air, gamma = 1.iv for standard solar day conditions. "Gamma" appears in many fluids equations including the equation relating pressure level, temperature, and volume during a unproblematic pinch or expansion process, the equation for the speed of sound, and all the equations for isentropic flows, and shock waves. Considering the value of "gamma" just depends on the country of the gas, in that location are tables of these values for given gases. You tin apply the tables to solve gas dynamics problems.

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Source: https://www.grc.nasa.gov/WWW/BGH/specheat.html

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