Which of the following is incorrect regarding the first law of thermodynamics?
(a) It is not applica

Q: Why is the change in internal energy zero in a cyclic process?

Internal energy is a 'state function', meaning its value depends only on the current pressure, volume, and temperature of the system. In a cyclic process, the system returns exactly to its starting state, so the final internal energy is the same as the initial internal energy, making the change zero.

Q: Does the First Law of Thermodynamics apply to all processes?

Yes! The First Law is a universal law of conservation of energy. It applies to isothermal, adiabatic, isobaric, isochoric, and cyclic processes without exception.

Q: What law introduces the concept of entropy?

The concept of entropy is introduced by the Second Law of Thermodynamics, which deals with the direction of heat flow and the irreversibility of natural processes.

Q: Why does the book's answer key say (d) is the correct option?

This is a known typographical error in the book. The solution mentions 'entropy', suggesting option (c) was originally printed as 'It introduces the concept of entropy' in the actual exam. With the options printed here, only (a) is an incorrect statement.

Q: Are heat and work state functions?

No, heat ($\Delta Q$) and work ($\Delta W$) are 'path functions'. Their values depend on the specific path or process taken between the initial and final states, not just the states themselves.

Question

Which of the following is incorrect regarding the first law of thermodynamics?

Options:

(A) It is not applicable to any cyclic process

(B) It is a restatement of the principle of conservation of energy

(C) It introduces the concept of the internal energy

(D) Both (a) and (c)

Sigma Percentile · Accepted Answer

### The Heart of Thermodynamics

Thermodynamics is the beautiful study of energy, heat, and work. At the very core of this subject lies the **First Law of Thermodynamics**, which is essentially the universe's ultimate accounting system. It states that energy cannot be created out of nothing, nor can it vanish into nothingness. It can only change forms.

Mathematically, we express this profound truth as:

$$\Delta Q = \Delta U + \Delta W$$

Here, $\Delta Q$ is the heat supplied to the system, $\Delta U$ is the change in the system's internal energy, and $\Delta W$ is the work done by the system. Let's break down the options provided in the question to see which one violates the laws of physics.

### Analyzing the Options

**Option (b): It is a restatement of the principle of conservation of energy.**
As we just discussed, the First Law is exactly that. If you give a system $100 	ext{ J}$ of heat energy, and it does $40 	ext{ J}$ of work, the remaining $60 	ext{ J}$ must be stored inside the system. Energy is perfectly conserved. Thus, statement (b) is absolutely correct.

**Option (c): It introduces the concept of the internal energy.**
Before the First Law was formalized, scientists understood heat and work, but the concept of a state variable that stores energy *within* the system was missing. The First Law formally introduces $\Delta U$, the internal energy, bridging the gap between microscopic kinetic/potential energy of molecules and macroscopic heat/work. Therefore, statement (c) is also correct.

### The Cyclic Process Mystery

**Option (a): It is not applicable to any cyclic process.**
Imagine a gas in a cylinder that expands, cools, compresses, and heats back up to its exact starting pressure, volume, and temperature. This is a **cyclic process**.

Because internal energy ($U$) is a **state function**, it depends only on the current state of the system, not how it got there. Since the initial and final states in a cyclic process are identical, the change in internal energy is zero:

$$\oint dU = 0 \implies \Delta U = 0$$

If we plug this into the First Law, we get:

$$\Delta Q = 0 + \Delta W \implies \Delta Q = \Delta W$$

This tells us that in a complete cycle, the net heat absorbed by the system is exactly equal to the net work done by the system. The First Law works perfectly here! Therefore, the claim that it is *not* applicable to cyclic processes is blatantly **false**. Statement (a) is the incorrect statement we are looking for.

### The Typo Uncovered

You might be wondering, if statement (a) is the only incorrect statement, why does the official answer key point to option (d), which claims both (a) and (c) are incorrect?

If we look closely at the reference solution provided in the source material, it states: *"Concept of entropy is associated with second law of thermodynamics."*

This is a massive clue! It implies that in the original exam paper, option (c) likely read: *"It introduces the concept of entropy."* If that were the case, option (c) would indeed be incorrect (since entropy comes from the Second Law), making both (a) and (c) incorrect, and justifying (d) as the correct choice.

However, as printed in this specific text, option (c) correctly mentions *internal energy*. Therefore, based strictly on the text in front of us, (a) is the only incorrect statement. Always trust the physics over a misprinted answer key!

Animated Solution for Physics - Thermodynamics: Which of the following is incorrect regarding the first law of thermodynamics?

Select Answer:

Visualized Solution

$The First Law of Thermodynamics$

$Conservation of Energy$

$Concept of Internal Energy$

$Cyclic Processes$

$Internal Energy in a Cycle$

$First Law for Cyclic Process$

$Addressing the Anomaly$

The Sigma Insight: First Law of Thermodynamics

The Heart of Thermodynamics

Analyzing the Options

The Cyclic Process Mystery

The Typo Uncovered

Similar Questions

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume non-expansion work is zero)

A heat engine absorbs heat $q_{1}$ from a source at temperature $T_{1}$ and heat $q_{2}$ from a source at temperature $T_{2}$ . Work done is found to be $J (q_{1} + q_{2})$ . This is in accordance with

For an ideal gas

For a diatomic ideal gas in a closed system, which of the following plots does not correctly describe the relation between various thermodynamic quantities?

A system goes from $A$ to $B$ via two processes I and II as shown in figure. If $Δ U_{1}$ and $Δ U_{2}$ are the changes in internal energies in the processes I and II respectively, then

A reversible cyclic process for an ideal gas is shown below. Here, P , V and T are pressure , volume and temperature , respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K, respectively. Choose the correct statement.

The internal energy change when a system goes from state $A$ to $B$ is $40 kJ/mol$ . If the system goes from $A$ to $B$ by a reversible path and returns to state $A$ by an irreversible path, what would be the net change in internal energy?

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is $- 180 J$ . The gas absorbs $250 J$ of heat along the path ab and $60 J$ along the path bc. The work done by the gas along the path abc is

Following figure shows two processes A and B for a gas. If $Δ Q_{A}$ and $Δ Q_{B}$ are the amount of heat absorbed by the system in two cases, and $Δ U_{A}$ and $Δ U_{B}$ are changes in internal energies respectively, then