# Law Of Thermodynamics Calculator

Thermodynamics Learning Material
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13.10Entropy and the Second Law of Thermodynamics

This online calculator can solve thermodynamic equilibrium problems, such as finding the final temperature when mixing fluids, or finding the required temperature for one of the fluids to achieve a final mixed temperature.

• The only condition is that there should not be any phase transition (or phase change) of substances.
• To solve the problem, it uses the thermal equilibrium equation, more on this below.
• In the process of reaching thermodynamic equilibrium, heat is transferred from the warmer to the cooler object.
• Two objects are in thermal equilibrium if no heat flows between them when they are connected by a path permeable to heat, that is, they both have the same temperature.
• This is called the zeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially and temporally uniform.
• The thermodynamic system is called a thermally isolated system if it does not exchange mass or heat energy with its environment.
• In physics, the law of conservation of energy states that the total energy of an isolated system in a given frame of reference remains constant — it is said to be conserved over time.
• The first law of thermodynamics can be stated as follows: during an interaction between a system and its surroundings, the amount of energy gained by the system must be exactly equal to the amount of energy lost by the surroundings.
• In the case of a thermally isolated system, we can say that during an interaction between objects inside a system (until it reaches thermal equilibrium), the amount of energy gained by one object must be exactly equal to the amount of energy lost by another.
• This is our thermal equilibrium equation. In another form:,where n – number of objects in the system.
• That is, the algebraic sum of all heat quantities (gained and lost) in a thermally isolated system equals zero.

## Physics Calculators

If we replace heat quantities with the formula described here: Quantity of heat, we will get the following equation:. ,note that the final temperature for all substances (T1, T2, .. Tn) should be the same, because of thermal equilibrium. This is the equation used by the calculator to find the unknown value. Also, the calculator can take into account the quantity of heat gained or lost to the surroundings.

This allows a more broad range of problems to be solved. To use the calculator, you need to correctly fill out the table describing interacting substances.

The usage instructions for different scenarios are listed below the calculator.

In this Physics tutorial, you will learn:. What is temperature? How the speed of molecules is related to temperature?

### Isobaric process

What are the devices used to measure the temperature? What are the units of temperature? How is the temperature related to the thermal energy of objects? What is thermal equilibrium? What does the Zeroth Law of Thermodynamics say? All us are quite familiar with the term "temperature". When we touch a hot object, we say "the object's temperature is high".

On the other hand, we consider the temperature of ice as low, as for us "the ice is cold." In a certain sense, we define temperature as "the degree of hotness in an object". But this definition is intuitive, and it makes reference to our senses. We cannot use this approach to determine correctly the degree of hotness, i.e.

the assign an exact numerical value to temperature. A cup of tea can be "warm" for one person who is inside the room and "very hot" for another person who is just entering house during a winter day.

Thus, we must find a universally applicable way to measure the numerical value of temperature, i.e. of the degree of hotness in an object.

In this tutorial, we will explain in detail the meaning of temperature along with its units and measuring devices.

Therefore, by the end of this tutorial, every doubt on this issue will be clarified. All particles of any object in whatever state it may be are in unceasing motion.

In general, they vibrate around some fixed points known as "equilibrium positions". It is obvious that faster the particles' vibration, greater their kinetic energy.

## Related Physics Calculators by iCalculator

It is impossible to measure the kinetic energy of all particles of an object due to the very big number of particles (but also because such motion is very irregular). Molecules of a objects may have a wide range of velocities, and furthermore, the speed of a molecule changes millions of times in a second due to the collisions with other molecules.

At a given instant one molecule may nearly be at rest while another molecule moves with almost the speed of light during vibrations. Consequently, the kinetic energies of molecules of an object are quite different. But an average value of their kinetic energy gives us an idea about the behavior of an object's particles, especially in gases.

Therefore, we use an indirect way to estimate the kinetic energy of an object's particles (in other words its thermal energy), which is one of the main components of their internal energy (the other is the chemical energy generated during chemical reactions). The only way to draw a correct conclusion regarding the objects' degree of hotness is by finding an appropriate way to measure their warmth. This is achieved by introducing a more direct measurement than particles' average kinetic energy.

As a result, a few centuries ago the concept of temperature was introduced. By definition, temperature represents a measure of the ability of a substance, or more generally of any physical system, to transfer heat energy to another physical system. Temperature as a concept is closely related to the average kinetic energy of all particles of the object or system.

This means temperature is a more suitable quantity related to the measurements of objects' warmth than heat energy, because its value can be measured directly through devices called thermometers.

## Introduction

A thermometer uses the expansive of contractive properties of liquids such as alcohol or mercury to show different values. But first, a thermometer needs to be graded. For this, a lower fixed point and an upper fixed point are needed. The process of assigning different values to different heights of liquid column in a thermometer is known as "calibration of thermometer".

Anders Celsius, a Swedish scientist introduced (in the eighteenth century) a practical method of thermometer calibration. He used the freezing and boiling points (temperatures) of water as a lower and upper fixed points respectively and then he decided to divide the range of temperatures between these two fixed points in 100 equal parts.

Each division is called 1-Celsius degree (1°C)and such a way of thermometer calibration is known as Celsius Scale.

Obviously, such a calibration can be extended even beyond these two fixed points as we know that in winter air temperatures can go below zero or melting process of metals needs temperatures much higher than 100°C.

On the other hand, Daniel Gabriel Fahrenheit, a German scientist, used the temperatures in the coldest and the hottest days in his country to calibrate thermometers. In this way, he invented the Fahrenheit Scale. The conversion formula between Celsius and Fahrenheit scales is: .

The weather forecast shows a value of 86° F for the next day.

What is the corresponding value in Celsius degree?

### Isochoric process

From the formula . t (°F) = 1.8 × t (°C) + 32°. we obtain after substituting the values:. 86 = 1.8 × t (°C) + 32 1.8 × t (°C) = 86 - 32 = 54 t (°C) = 54 / 1.8 t (°C) = 30°C.

1. However, the official SI unit of temperature is none of the above but Kelvin Scale.
2. It is named after the Lord Kelvin, alias William Thompson, the Scottish famous scientist.
3. Kelvin degree is the SI unit of temperature as it offers a great advantage compared to the other units: it has only positive (or zero) values because the lower fixed point of this scale refers to the lowest temperature in the universe, i.e.

### Temperature and Thermal Equilibrium. The Zeroth Law of Thermodynamics

the temperature in which particles of matter stop vibrating around their equilibrium positions.

When measured in Celsius degree, this minimum temperature is equal to -273.16°C. Therefore, we can write: .

or more generally,. T(K) = t (°C) + 273°. The division method is the same in both Celsius and Kelvin degrees, only the lower fixed points are different. This means an increase in temperature by 5°C for example, represents an increase in temperature by 5 K as well.

Convert the following temperatures into the required ones: . t (°F) = 1.8 × t (°C) + 32° 5 = 1.8 × t (°C) + 32 1.8 × t (°C) = 5 - 32 = -27 t (°C) = -27 / 1.8 t (°C) = -15°C.

When converted this value into Kelvin degree, it becomes. b) First, let's convert the temperature from Kelvin to Celsius Scale.

Thus, given that. T(K) = t (°C) + 273°.

we obtain, after substitutions for the temperature in Celsius scale,. 373° = t (°C) + 273° t (°C) = 373° - 273° = 100°C. Unlike in the other two scales, in Kelvin scale temperature is denoted by capital T instead of t.

## What are thermodynamic processes? Combined gas law formula

Also, the symbol of degree (°) is not written in Kelvin scale. As written in the definition, temperature represents a measure of the ability of an object or a system of objects to transfer heat energy to another object or system. But before explaining what this definition really means, it is necessary to explain a few concepts, such as heat energy, thermal energy, internal energy and heat transfer.

Objects possess energy in a variety of forms. Some types of energy are easily visible and measurable such as kinetic energy, gravitational potential energy and elastic potential energy we have explained earlier in Section 5.

However, there are some other types of energy the objects possess in a microscopic form, which are not easy to be identified and calculated.

These energies belong to the category of internal energy. The two main subcategories of internal energy are chemical and thermal energy.

The first involves the energy generation or absorption during chemical reactions. The later involves the energy generation during the local movements (like vibrations) of objects' particles due to their hotness, as explained earlier.

Therefore, it is easy to conclude that thermal energy is somehow related to temperature, i.e. hot objects possess more thermal energy than cold objects as their particles vibrate more rapidly.

The part of this thermal energy that is transferred to another object, is known as heat energy.

## The Molecular Meaning of Temperature

As explained in the Physics tutorial 5.1 "Work and Energy. Types of Energy", heat can be transferred from one object into another when the proper conditions are created.

One condition would be putting a hot and a cold object in contact to each other and thus, paving the way to the heat energy to transfer from the hottest object to the coldest one. There is not any matter transfer during this process; the only thing that is transferred is the heat energy due to the collision pf particles in the bordering parts between the two objects.

Faster particles in the outer layer of the hot object collide with the slower particles of the outer layer of the cold object. In this way, the hot object loses some heat energy as its particles get slower during the collision and the cold object gains some heat energy because its particles become faster during the collision with more energetic particles.

As a result, there is a heat exchange between objects which eventually bring a change in the internal energy of both objects.

The heat "flow" eventually stops when both objects have reached the same temperature.

This means the average speeds of particles vibration in both objects are already equal. In other words, the heat flow stops when thermal equilibrium is established.

In this way, we obtained the meaning of thermal equilibrium, i.e.

a condition in which all parts of a system are at the same temperature.

It is precisely on this concept that the Zeroth Law of Thermodynamics is based.

It states that: . If a thermodynamic system A is in thermal equilibrium with another thermodynamic system B and the thermodynamic system B is in thermal equilibrium with a third thermodynamic system C, then the thermodynamic system A is also in thermal equilibrium with the thermodynamic system C.

A thermodynamic system is an object of a group of objects with the same temperature. For simplicity, we will consider the system as a single object.

### Isothermal process

Thus, in simpler words, the Zeroth Law of Thermodynamics says: . If an object A has the same temperature with another object B and the object B has the same temperature with a third object C, then the object A has the same temperature with the object C.

For example, the object in the factory in which a thermometer was originally placed in contact to do its calibration represents the system A, the thermometer itself is the system B and the patient's body is the system C.

The Zeroth Law of Thermodynamics is schematically shown below. It is called the "Zeroth Law of Thermodynamics" as it was formulated after the First and the Second Laws of Thermodynamics, for which we will discuss in the next tutorials.

Enjoy the "Temperature.

The Zeroth Law of Thermodynamics" physics tutorial?

### First law of thermodynamics

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## Units of Temperature

At constant temperature, the product of the pressure, \(P\), and volume, \(V\), of an ideal gasis constant: \$\$P_1 V_1=P_2 V_2\$\$ . At constant pressure, the volume of an ideal gas is directly proportional to its temperature.

\$\$V_1\,/\,T_1=V_2\,/\,T_2\$\$ . The pressure exerted on the sides of a container by an ideal gas of fixed volume is proportional to its temperature.

\$\$P_1\,/\,T_1=P_2\,/\,T_2\$\$ . Combine all of the laws above, and get the "ideal gas law": \$\$PV = nRT \, \, \textrm{or}\,\,\, PV = kNT \,\$\$ where \(P\) is pressure in Pascals, \(V\) is volume in Liters, \(n\) is number of moles, \(R\) is universal gas constant, \(T\) is temperature in Kelvin, \(k\) is the Boltzmann constant and \(N\) is the number of gas molecules.

Corrections to this equation are needed for real gasses, dependent on their molar weight and volume.

All values must be in SI units (as given above), because the constants, R and k, are in the units J/K/mol and J/K respectively.

Defaults are set to standard temperature and pressure and a 1 liter volume.

• The "hits/time" on the piston are what creates the pressure. More particles = more overall hits.
• Faster particles means more hits in a given time period. Less volume means particles are more likely to hit the piston.
• Move the sliders below to independently change the variables V, N, and T. The gauge on the right shows the effect of the changes on the pressure.

Note: this simulation is still a work in progress. Your browser does not support HTML5 Canvas!

While we have done our best to ensure accurate results, the authors of this website do not make any representation or warranty, express or implied, regarding the calculators on this website, nor assume any liability for its use. The code implementation is the intellectual property of the developers. Please let the webmaster know if you find any errors or discrepancies. We also take suggestions for new calculators to include on the site. Reviewed byBogna Szyk. Combined gas law calculator is a great tool to deal with problems related to the most common transformations of gases.

Read about isobaric, isochoric, isothermal, and adiabatic processes of ideal gases (gases that can be described by the ideal gas equation).

1. And how it is possible for the ideal gases to do work or release/absorb heat.
2. Check out the exact values for real gases and forget about struggling with thermodynamic exercises!

An ideal gas can be described by several parameters, which are pressure p, volume V, temperature T and the amount of particles n.

They are correlated with the equation: p * V = n * R * T, where R stands for ideal gas constant and equals 8.3144598 J/(mol * K). During any process at least two of these properties change which can be compiled in combined gas law formula: p * V / T = k, where k is a constant.

### Computational example

Out of all transformations, we can distinguish a few which encompass a vast majority of examples from everyday life, or they can be treated as good approximations.

### Whats next?

In this combined gas law calculator, we consider processes in which the number of particles is constant, thus we can imagine a gas in a closed container. isochoric process,. isobaric process,. isothermal process,. adiabatic process. Internal energy U is the sum of all kind of energies that are present in a system.

It's quite tricky to estimate the precise value of internal energy, but it is possible to find thermal energy changesΔU, which are described by the first law of thermodynamics: ΔU = Q - W, where Q denotes heat absorbed, and W is work done by gas.

Internal energy change is proportional to temperature variation ΔT and type of gas with the following equation: ΔU = Cv * n * ΔT, where Cv is molarheat capacity under constant volume.

For ideal gas it takes values:. 3/2 * R for monoatomic gas,. 5/2 * R for diatomic gas,. 3 * R for gases with more complex molecules. In real gases, these parameters differ from theoretical ones, but it's already contained in our thermodynamic processes calculator.

## Carnot cycle

The general formula for work done by the gas is expressed as: ∫p(V)dV if we consider pressure as the function of volume. Although it isn't trivial in general, you can check how the formula simplifies for processes mentioned below.

1. During this transition volume is a constant parameter, so that initial properties p₁, T₁ changes to p₂, T₂ as follows: p₁ / T₁ = p₂ / T₂.
2. The invariability of volume means that gas doesn't do any work and the heat absorbed by gas is precisely the same as internal energy change: ΔU = Q = Cv * n * ΔT. This process can be visualized for gas kept in a rigid container, but which can exchange heat with an environment.
3. Gay-Lussac's lawcorresponds to this thermodynamic process. It is assumed that pressure is a constant gas parameter during this transition. Therefore the initial parameters V₁, T₁ transform to V₂, T₂with the following form of combined gas law formula: V₁ / T₁ = V₂ / T₂.
4. Due to the fact that pressure is invariant, the formula for work done by the gas is given by: W = p * ΔV. Heat, however, can be calculated as: Q = ΔU + W = Cv * n * ΔT + p * ΔV = Cp * n * ΔT.
5. Cp is known as molar heat capacity under constant pressure, and for an ideal gas is associated with Cv, so that Cp = Cv + R.

## Calculate with ideal gas law

Charles' lawis related to this transition. The constant parameter in this transition is temperature so that initial properties p₁, V₁ change to p₂, V₂, and the correlation is: p₁ * V₁ = p₂ * V₂.