A given quantity of gas is taken from A to C in two ways; a) directly from A\(\rightarrow\)C along a straight line and b) in two steps, from A\(\rightarrow\)B and then from B\(\rightarrow\)C.Work done and heat absorbed along the direct path A\(\rightarrow\)C are 200J and 280J respectively. If the work done along A\(\rightarrow\)B\(\rightarrow\)C is 80J, then heat absorbed along the path is,
- 80J
- 0
- 160J
- 120J
The Correct Option is C
Approach Solution - 1
While moving along path AC, the change in internal energy (dU) is determined by the difference between heat (dQ) added to the system and work (dW) done by the system. In this case, dU=dQ−dW=300−200=100J. This illustrates that internal energy is a point function, which means it remains consistent across all paths.
Along path ABC, the heat (dQ) is the sum of the change in internal energy (dU) and the work (dW) done on the system.
The correct option is(C) 160J
Approach Solution -2
Given Data:
1. Work done along the direct path A → C (\(W_{AC}\)) = 200 J
2. Heat absorbed along the direct path A → C (\(Q_{AC}\)) = 280 J
3. Work done along the path A → B → C (\(W_{ABC}\)) = 80 J
Using the first law of thermodynamics for the direct path A → C:
\[ \Delta U = Q_{AC} - W_{AC} \]
Substituting the given values:
\[ \Delta U = 280 \, \text{J} - 200 \, \text{J} = 80 \, \text{J} \]
This change in internal energy (\(\Delta U\)) is the same for both paths A → C and A → B → C since internal energy is a state function and depends only on the initial and final states, not on the path taken.
Calculating Heat Absorbed Along Path A → B → C:
Using the first law of thermodynamics again for the path A → B → C:
\[ \Delta U = Q_{ABC} - W_{ABC} \]
We know \(\Delta U\) (from the direct path A → C) and \(W_{ABC}\):
\[ 80 \, \text{J} = Q_{ABC} - 80 \, \text{J} \]
Solving for \(Q_{ABC}\):
\[ Q_{ABC} = 80 \, \text{J} + 80 \, \text{J} = 160 \, \text{J} \]
Conclusion:
The heat absorbed along the path A → B → C is 160 J.
Therefore, the correct option is (C) 160 J.
Top Questions on Thermodynamics
- Given are statements for certain thermodynamic variables: \begin{itemize} \item[(A)] Internal energy, volume \( V \), and mass \( M \) are extensive variables. \item[(B)] Pressure \( P \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(C)] Volume \( V \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(D)] Mass \( M \), temperature \( T \), and internal energy are extensive variables. \end{itemize} Choose the correct answer from the options given below:
- JEE Main - 2025
- Physics
- Thermodynamics
- For a diatomic gas, if \( \gamma_1 = \frac{C_P}{C_V} \) for rigid molecules and \( \gamma_2 = \frac{C_P}{C_V} \) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (where \( C_P \) and \( C_V \) are specific heats of the gas at constant pressure and volume)
- JEE Main - 2025
- Physics
- Thermodynamics
- Match List - I with List - II. List - I (Partial Derivatives) \(and\) List - II (Thermodynamic Quantity)
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Chemistry
- Thermodynamics
- A container of fixed volume contains a gas at 27°C. To double the pressure of the gas, the temperature of the gas should be raised to °C.
- JEE Main - 2025
- Physics
- Thermodynamics
- The work done in an adiabatic change in an ideal gas depends upon:
- JEE Main - 2025
- Physics
- Thermodynamics
Questions Asked in WBJEE exam
- Two straight conducting plates form an angle θ where their ends are joined. A conducting bar in contact with the plates and forming an isosceles triangle with them, starts at the vertex at time t = 0 and moves with constant velocity v to the right as shown in the figure. A magnetic field B points out of the page. The magnitude of emf induced at t = 1 second will be:
- WBJEE - 2024
- Electromagnetic induction
- A 2V cell is connected across the points A and B as shown in the figure. Assume that the resistance of each diode is zero in forward bias and infinity in reverse bias. The current supplied by the cell is:
- WBJEE - 2024
- Current electricity
- Consider a circuit where a cell of emf \( E_0 \) and internal resistance \( r \) is connected across the terminal A and B as shown in the figure. The value of \( R \) for which the power generated in the circuit is maximum, is given by:
- WBJEE - 2024
- Current electricity
- In a series LCR circuit, the rms voltage across the resistor and the capacitor are \(30 \, \text{V}\) and \(90 \, \text{V}\) respectively. If the applied voltage is \(50\sqrt{2}\sin\omega t\), then the peak voltage across the inductor is:
- WBJEE - 2024
- Alternating current
- Which of the following statement(s) is/are true in respect of nuclear binding energy?
(i) The mass energy of a nucleus is larger than the total mass energy of its individual protons and neutrons.
(ii) If a nucleus could be separated into its nucleons, an energy equal to the binding energy would have to be transferred to the particles during the separating process.
(iii) The binding energy is a measure of how well the nucleons in a nucleus are held together.
(iv) The nuclear fission is somehow related to acquiring higher binding energy.- WBJEE - 2024
- Nuclear physics
Concepts Used:
Thermodynamics
Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.
Important Terms
System
A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.
There are three types of systems:
- Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
- Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
- Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.
Thermodynamic Process
A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.
There are four types of thermodynamic process that have their unique properties, and they are:
- Adiabatic Process – A process in which no heat transfer takes place.
- Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
- Isobaric Process – A process in which no change in pressure occurs.
- Isothermal Process – A process in which no change in temperature occurs.
Laws of Thermodynamics
Zeroth Law of Thermodynamics
The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.
First Law of Thermodynamics
The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.
Second Law of Thermodynamics
The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.
Third Law of Thermodynamics
Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.