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First Law of Thermodynamics - Statement, Equation, Limitations, Practice Problems and FAQs

First Law of Thermodynamics - Statement, Equation, Limitations, Practice Problems and FAQs

Suppose you are walking to your home and started feeling tired while walking and you are completely exhausted once you reached home and without waiting you just want to turn on the fan, sit back and relax for a while. 

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What do you think about how much of the energy you have destroyed? Wait! did I just say energy is getting destroyed? Guess I have asked the wrong question. This is a misconception that many of us have.

We know that when we walk the energy stored in our body is used to do work and as a result of this mechanical work that we did, the body gets heated up.

As we can see here it’s the chemical energy (food) that gets converted into mechanical energy (walk) which in turn gets converted into heat energy (rise in body temp). So, one can say that energy is converted from one form to another one form of energy gets changed into another , it's not like it's getting destroyed and this is actually a statement of the first law of thermodynamics. 

Table of contents

  • Statement of First Law of Thermodynamics
  • Equation of First Law of Thermodynamics
  • Sign Conventions
  • Limitations of First Law of Thermodynamics
  • Perpetual Motion Machine of First Kind (PMM-I)
  • First Law of Thermodynamics for a Closed System
  • Practice Problems
  • Frequently Asked Questions-FAQs

Statement of First Law of Thermodynamics

The first law of thermodynamics states that energy can neither be created nor destroyed, but can be transformed from one form to another. This is also known as the law of conservation of energy. In other words, the total energy of the universe remains constant. Alternatively said, the universe's overall energy remains constant.

A thermodynamic system in an equilibrium state possesses a state variable known as internal energy (U). 

Internal energy (U) is a state variable that exists in a thermodynamic system at equilibrium . Between two systems the change in the internal energy is equal to the addition of both heat transfer and the work done. 

Equation of First Law of Thermodynamics 

The equation for the first law of thermodynamics is given as;

The first law of thermodynamics' equation is as follows:
ΔU = q + W
Where
ΔU = change in internal energy of the system ΔU represents the system's internal energy change.
q = is the algebraic sum of heat transfer between system and surroundings
W = work interaction between the  of the system with the it’s  surroundings

Sign Conventions

The table below shows the appropriate sign conventions for all three properties under different conditions. 

Heat (q)

Work done (W)

Heat transferred to the system; q=+ve

Work done to the system; W=+ve

Heat transferred to the surroundings; q=-ve

Work done by the system; W=-ve


Now, let's consider various cases of expansion, compression, cooling and heating a system. 

Case I: Compression and heating

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As demonstrated above, the gas inside the cylinder is being heated, and the weight above the piston is steadily increasing. Even after a rise in internal pressure due to heating, the weight on the piston is constantly raised, causing the gas to compress. The system's surroundings perform the compression work.

Therefore, W = +ve.
Also, heat is given to the system.
Therefore, q = +ve.
We have,
ΔU = q + W
Since both q and W are positive,
ΔU is also positive.

Case II: Expansion and cooling

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The gas is being cooled and the piston is moving upwards. For expansion, work is done by the system. Therefore, W = -ve.
Also, heat is released/dissipated by the system since it is being cooled.
Hence, q = -ve
We have,
ΔU = q + W

Since both q and W are negative, ΔU is also negative.

Case III: Compression and cooling

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The gas inside the cyllinder is being cooled, and the weight above the piston is steadily increasing. Even after the temperature of the gas is decreased by removing heat out of the system, the weight on the piston is constantly raised, causing the gas to compress. The system's surroundings perform the compression work.

Work is done on the system for compression.
Therefore, W = +ve.
Since it is cooled, heat is released/dissipated by the system.
Therefore, q = -ve.

In this case, ΔU can be positive or negative as it depends on the magnitude of q and W.

Case IV: Expansion and heating

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The gas inside the cylinder is being heated and work is done by the system for expansion.
Therefore, W = -ve
Since it is heated, heat is given to the system.|
Therefore, q = +ve

In this case, ΔU can be positive or negative as it depends on the magnitude of q and W.

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Limitation of First Law of Thermodynamics

When a system goes through a thermodynamic process, it must always maintain a specific energy balance, according to the law. The law states that a system must always maintain a particular energy balance while undergoing a thermodynamic process. The first law, on the other hand, On the other hand, the first law ignores the system's ability to change state or process.

When a metallic rod is heated at one end but not the other, for example, the first law fails to explain why heat transfers from the hot end to the cold end for instance, the first law, is unable to explain why heat transfers from the hot end to the cold end. The first law merely measures the amount of energy transferred during this process Just how much energy is transmitted throughout this process is measured by the first law. The second law of thermodynamics is the criterion for determining the feasibility of thermodynamic processes and suggests the spontaneity of the process. 

Perpetual Motion Machine of First Kind (PMM-I)

It is impossible to construct a machine that can continuously supply mechanical work without consuming any energy simultaneously. Such a hypothetical machine is known as the perpetual motion machine of the first kind. These types of machines violate the first law of thermodynamics and do not exist in reality.

First law of Thermodynamics for a Closed System

Thermodynamics' First Law for a Closed System

Work done for a closed system is the product of external pressure applied and the change in volume that occurs due to external pressure. 

The product of amount of external pressure that is used and the volume that changes as a result of that pressure are what provide the work for a closed system.

W = − PextΔV

Where Pext is the constant external pressure on the system, and ΔV is the change in volume of the system. This is specifically called “pressure-volume” work.

Where ΔV is the change in the system's volume and Pext is the continuous external pressure on the system. This is known as "pressure-volume" work.

Now according to the first law of thermodynamics; 
ΔU = q + W
Putting the value of work done; W = −PextΔV ;
ΔU = q −PextΔV

The internal energy of a system increases or decreases depending on work interaction that takes place across its boundaries. The internal energy would increase if work is done on the system and decreases if work is done by the system. Any heat interaction that takes place between the system and surroundings also changes its internal energy. Any heat exchange that occurs between a system and its surroundings also alters the system's internal energy.

Practice problems

Q1. 110 J of heat is added to a gaseous system and 130 J of work is done by the system, whose initial internal energy is 40 J. Final internal energy of the system is: 

A) -40 J 
B) -20 J 
C) 20 J 
D) 40 J

Answer:  (C) 

Solution: Given; 

q =+110 J (as heat is added to the system)
W=-130 J (as work is done by the system)
Ui= 40 J

According to the first law of thermodynamics, we can write:

U = q + W
U- U= q + W
U= U+ q + W
U= 40 + 110 + (-130) J
U= 20 J

Q2. A system has constant volume (ΔV=0) and the heat of the system increases by 45 J. A system's heat increases by 45 J while its volume remains constant (ΔV=0) .

  1. What is the sign convention for heat transfer (q)?
  2. What is the value of change in the internal energy of the system in Joules?

What is the change in the system's internal energy in Joules?

Solution:

  1. negative (q < 0), as heat is given to the system. 
  2. According to the first law of thermodynamics;

U =q +W
ΔU = q + (-PΔV) = q+ 0 (at constant volume, ΔV=0)

Given the value of heat transfer, q=-45J
So, ΔU =q=-45J

Q3. A process occurs at constant pressure. The surroundings around the system lose 60 J of heat and 440 J of work is done on the system. The system exerts 440 J of work while the surroundings lose 60 J of heat.The change in the internal energy of the system is: The system’s internal energy change is :

A) 500 J
B) -500 J
C) -380 J
D) 380 J

Answer: (A)

Solution :

Given; 
q =+60 J (as heat is added to the system because surroundings lose heat)
W=+440 J (as work is done by the system)

According to the first law of thermodynamics, we can write:

U =q +W
ΔU = (60 J) + (440 J)
ΔU = 500 J

Q4. In a system, a piston caused an expansion against an external pressure of 1.5 atm giving a change in the volume of 30 L for which ΔU=-40 kJ. The value of the heat evolved is: 

A piston in a system induced an expansion in response to an external pressure of 1.5 atm, changing the volume of the system by 30 L, with ΔU=-40 kJ. The heat evolved has the following value:

(Take 1 L-atm ≈ 100 J)

A) 36 kJ 
B) 13 kJ 
C) 5 kJ 
D) 24 kJ

Answer: (C)

Solution: At constant external pressure, we have,

W = -Pext.ΔV
= -1.5 atm × 30 L =-45 L-atm
= -45 × 100 J=-4500 J =-4.5 kJ (1 L atm ≈ 100 J)

According to the first law of thermodynamics, ΔU = q + W

Then, q = ΔU - W
= -40 kJ - (-4.5 kJ)
= -35.5kJ

So the value of heat evolved out of the system is 35.5 kJ.

Frequently Asked Questions (FAQs)

Question 1. Which law of thermodynamics is known as the law of energy conservation?
Answer: The first law of thermodynamics is also known as the Law of Conservation of Energy . Energy cannot be created or destroyed, according to the rule of conservation of energy.states that energy can neither be created nor destroyed; Energy can only be transferred from one form to another.

Question 2. Who stated the first law of thermodynamics?
Answer: Rudolf Clausius and William Thomson stated the first law of thermodynamics. According to this, energy can neither be created nor destroyed. In terms of the equation, it is;

ΔU = q + W
Where,
ΔU = change in internal energy of the system ΔU represents the system's internal energy change.
q = is the algebraic sum of heat transfer between system and surroundings
W = work interaction between the  of the system with the it’s  surroundings

Question 3. Can the first law of thermodynamics be violated?
Answer: A machine called a Perpetual Motion Machine of the first kind violates the first law by creating energy. It is a machine that can continuously supply mechanical work without consuming any energy simultaneously. So, clearly, energy is being created here, which is a violation of the first law of thermodynamics

Question 4. What is the best application of the first law of thermodynamics?
Answer: The most common practical application of the first law of thermodynamics is the heat engine. Heat engines convert thermal energy into mechanical energy. Most heat engines fall into the category of open systems. 

The heat engine is the device that uses the first law of thermodynamics the most frequently. Thermal energy is transformed into mechanical energy by heat engines. Open systems are what the majority of heat engines fall under.

Related Topics:

Isothermal Process

Thermodynamic Terms

Thermodynamic Processes

Degrees of Freedom

Heat Capacity Cp Cv relation

Zeroth Law of Thermodynamics

Second Law of Thermodynamics

Third Law of Thermodynamics

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