THERMODYNAMICS: October 2019

First law of Thermodynamics

Thermodynamics Process

The system (the gas) starts from an initial State i, described by pressure pi, a volume Vi, and a temperature Ti, You want to change the system to a final state f, described by a pressure from its initial state to its final state is called thermodynamic process. During such a process, energy may be transferred into the system from the thermal reservoir (positive heat) or vice versa (negative heat). Also, work can be done by the system to raise the loaded piston(positive work) or lower it (negative work). We assume that all such changes occur slowly, with the result that the system is always in (approximate) thermal equilibrium(every part is always in thermal equilibrium).

To further understand Thermodynamics Processes, Watch this video:

Total work done by the gas is

During the volume change, the pressure and temperature may also change.To evaluate the equation above, we would need to know how pressure varies with volume for the actual process by which the system changes from state i to state f.

Pressure-Volume Diagrams (PV diagrams) are useful tools for visualizing the thermodynamic processes of gases. These diagrams show pressure on the y-axis, and volume on the x-axis, and are used to describe the changes undergone by a set amount of gas. Because the amount of gas remains constant, a PV diagram not only tells you pressure and volume, but can also be used to determine the temperature of a gas when combined with the ideal gas law.

(a) The shaded area represents the work W done by a system as it goes from an initial state to a final state f. Work Wis positive because the system’s volume increases. (b) W is still positive, but now greater. (c) W is still positive, but now smaller. (d) W can be even smaller (path icdf ) or larger (path ighf). (e) Here the system goes from state f to state i as the gas is compressed to less volume by an external force.The work W done by the system is now negative. (f) The net work W net done by the system during a complete cycle is represented by the shaded area.

Example:

1.Using the PV diagram at right, find the amount of work required to transition from state A to B, and then the amount of work required to transition from state B to state C.

First law of Thermodynamics

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

Internal energy of the material depends only on the material’s state (Heat, temperature, pressure, and volume). Heat is the energy exchanged between the system and its surroundings. Hear is positive if the system absorbs heat and negative if the system loses heat. Work done by the system is positive if the system expands against an external force from the surroundings and negative if the system contracts because of an external force.

Example:

1.Five thousand joules of heat is added to a closed system, which then does 3000 joules of work. What is the net change in the internal energy of the system?

Some Special Cases of the First Law of Thermodynamics
1. Adiabatic processes. An adiabatic process is one that occurs so rapidly or occurs in a system that is so well insulated that no transfer of energy as heat occurs between the system and its environment.Putting Q=0 in the first law yields:

2. Isochoric or Constant-volume processes. If the volume of a system (such as a gas) is held constant, that system can do no work. Putting W= 0 in the first law yields:

3. Isobaric processes. It is a process which occurs at constant pressure. When the system is heated the volume goes up and piston moves upwards so the system does work and when the piston goes down you do work to the system making the volume goes down.

4. Isothermal processes- This process occurs at a constant temperature, this typically occurs when a system is in contact with an outside thermal reservoir, and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange.

5. Cyclical processes. There are processes in which, after certain interchanges of heat and work, the system is restored to its initial state. In that case, no intrinsic property of the system—including its internal energy—can possibly change. Putting ΔEint = 0 in the first law yields:

6. Free expansions. These are adiabatic processes in which no transfer of heat occurs between the system and its environment and no work is done on or by the system. Thus,Q = W = 0, and the first law requires that:

To learn more about Thermodynamics watch these videos:

TEMPERATURE

HEAT

1ST LAW OF THERMODYNAMICS

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Reference:

David Halliday, Jearl Walker, and Robert Resnick, Fundamentals of Physics 10^th edition

https://www.youtube.com/watch?v=dHdlH3l8FkM

https://www.youtube.com/watch?v=uyEwWZVSIrA

https://aplusphysics.com/courses/honors/thermo/thermodynamics.html

https://www.youtube.com/watch?v=4i1MUWJoI0U

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Heat

Based on our own perceptions, it's hard to perceive what it is exactly, For a long time, Scientists described heat as a kind of fluid because it's flow from one system to another but these days we actually known that Heat is not actually a fluid.

Heat is energy that is transferred between a system and its environment because of a temperature difference between them. In Equations we represents heat as "Q". It can be measured in joules (J), calories (cal), kilocalories (Cal or kcal), or British thermal units (Btu).

This video can help you to visualize the concept of heat:

The Absorption of Heat by Solids and Liquids

Heat capacity

The heat capacity C of an object is the proportionality constant between the heat Q that the object absorbs or loses and the resulting temperature change of the object that is:

The word “capacity” in this context is really misleading in that it suggests analogy with the capacity of a bucket to hold water. That analogy is false, and you should not think of the object as “containing” heat or being limited in its ability to absorb heat. Heat transfer can proceed without limit as long as the necessary temperature difference is maintained.The object may, of course, melt or vaporize during the process.

Specific heat

Specific heat c that refers not to an object but to a unit mass of the material of which the object is made. can replace the Heat capacity in the previous equation making it:

Heats of Transformation

When energy is absorbed as heat by a solid or liquid, the temperature of the sample does not necessarily rise. Instead, the sample may change from one phase, or state,to another.

The amount of energy per unit mass that must be transferred as heat when a sample completely undergoes a phase change is called the heat of transformation L.Thus, when a sample of mass m completely undergoes a phase change, the total energy transferred is:

When the phase change is from liquid to gas (then the sample must absorb heat) or from gas to liquid (then the sample must release heat), the heat of transformation is called the heat of vaporization L_v.

When the phase change is from solid to liquid (then the sample must absorb heat) or from liquid to solid (then the sample must release heat), the heat of transformation is called the heat of fusion L_f.

Examples:

1. An aluminium plate with a mass of 1.5kg. Calculate the thermal energy stored in the plate when the temperature rises from 20°C to 200°C. The specific heat capacity of aluminium is 913 J/kg° C.

2. If it takes 41000 joules of heat to melt 200 grams solid copper to liquid copper, what is the heat of fusion of copper?

3.How much heat is required to change 1.0 kg of ice, originally at –20.0°C, into steam at 110.0°C? Assume 1.0 atm of pressure. Using these values:

For more explained problems, Watch these videos:

TEMPERATURE

HEAT

1ST LAW OF THERMODYNAMICS

JUMP TO QUIZ

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Reference:

David Halliday, Jearl Walker, and Robert Resnick, Fundamentals of Physics 10^th edition

https://drive.google.com/file/d/127V7JVlcMDU7RnUy0kXIjCkfrlc5D6yw/view

http://www.cabrillo.edu/~jmccullough/Example_Problems/Temperature_Heat_Solutions.PDF

https://sciencenotes.org/heat-fusion-example-problem/

https://www.youtube.com/watch?v=dxtz2POUTJE

https://www.youtube.com/watch?v=AVYbTI73wSU

https://www.youtube.com/watch?v=ePm_N6RgLfk

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Temperature

Temperature expresses the hotness or coldness of a body, it is one of the seven SI base quantities. The equipment used to measure temperature is called thermometer.
Physicists measure temperature on the Kelvin scale, which is marked in units called kelvins. Kelvin scale is an Absolute scale It is expected to have no negative value and Kelvin scale doesn't have degrees unlike Celsius and Fahrenheit temperature scales.

Nearly all of the other countries in the world uses Celsius scale or formerly known as centigrade scale while United States uses Fahrenheit scale.

Temperature of a body has no upper limit but it does have a lower limit, This lower limit is called the Absolute zero and it is taken as the zero of the Kelvin.

Here, We have the comparisons of the different Temperature scales.

Since, We have different temperature scales we should learn how to convert from one scale to another.

Kelvin to Celsius:

Celsius to Fahrenheit:

Examples:
1. Aluminum metal melts at 660.37 C. What is the temperature in Kelvin?

2. The title of the book "Fahrenheit 451" refers to the temperature that book paper burns, or 451 F. What is the temperature in Celsius?

3. Room temperature is often used in calculations as 300 K. What is the temperature in Fahrenheit?

Temperature as measure of kinetic energy

Another definition of Temperature is a measure of how much kinetic energy - that is, energy in motion is in a system. The hotter the system is, It has more kinetic energy because it's atoms and molecules moving around.

Let's watch this little experiment to visualize the above definition:

The average kinetic energy of the particles is directly related to the temperature of the object by the following equation:

Examples:

1. Given that the average kinetic energy of the particles comprising our sun is 1.2×10^-19J, find the temperature of the sun.

The easiest way to figure out if there is a difference in temperature between two systems is through heat transfer "The hotter system will always transfer heat to the colder one. And if there is no heat transfer in a system at all, It is called Thermal Equilibrium.

But normally there will be some Heat transfer because that is how temperature of a system change. When temperature of a system changes it will undergo "thermal expansion" An increase in temperature can make solid expands and a decrease in temperature make it contracts. There are two ways on how a dimension of a solid may change it can decrease or increase in length(1-dimensional) or it can decrease or increase in volume(3 Dimensional).

Thermal Expansion

The properties of many bodies change as we alter their temperature, perhaps by moving them from refrigerator to a warm oven.

To give a few examples: As their temperature increases, the volume of a liquid increases, a metal rod grows a little longer, and the electrical resistance of a wire increases, as does the pressure exerted by a confined gas.

Let's watch these two struggle opening the pickle jar...

See? even "Mr. Big guy" at the GIF can't open the pickle Jar! Maybe because they skipped Thermodynamics class!

but kidding aside, you can often loosen a tight metal jar lid by holding it under a stream of hot water both the metal of the lid and the glass of the jar expand as the hot water adds energy to their atoms.(With the added energy, the atoms can move a bit farther from one another than usual, against the spring-like interatomic forces that hold every solid together.) However, because the atoms in the metal move farther apart than those in the glass, the lid expands more than the jar thus is loosened.

Linear Expansion

If the temperature of a metal rod of length L is raised by an amount ΔT, its length is found to increase by an amount

Volume Expansion

If the temperature of a solid or liquid whose volume is V is increased by an amount ΔT, the increase in volume is found to be:

The coefficients of volume expansion and linear expansion for a solid are related by:

Examples:

1. An aluminum rod has a length of exactly one meter at 300K. How much longer is it when placed in a 400°C oven? when coefficient of linear expansion of aluminum is 23x10^-6 per Kelvin.

2. A glass of water with volume 1 liter is completely filled at 5°C. How much water will spill out of the glass when the temperature is raised to 85°C?when coefficient of volume expansion of water is 207x10^-6 per °Celsius. and 27x10^-6 per °Celsius for the glass.