An ideal gas undergoes a cyclic transformation starting from point A and coming back to the same point by tracing the path A→B→C→D→A as shown in the three cases below.
Choose the correct option regarding \(\Delta U\):
An ideal gas undergoes a cyclic transformation starting from point A and coming back to the same point by tracing the path A→B→C→D→A as shown in the three cases below.
Choose the correct option regarding \(\Delta U\):
Show Hint
- \(\Delta U({Case-III})>\Delta U({Case-II})>\Delta U({Case-I})\)
- \(\Delta U({Case-I}) = \Delta U({Case-II}) = \Delta U({Case-III})\)
- \(\Delta U({Case-I})>\Delta U({Case-II})>\Delta U({Case-III})\)
- \(\Delta U({Case-I})>\Delta U({Case-III})>\Delta U({Case-II})\)
The Correct Option is B
Solution and Explanation
- For a cyclic process, the internal energy change (\(\Delta U\)) is always zero as the system returns to its initial state.
- Since \(\Delta U\) is a state function, it depends only on the initial and final states, which are the same for all three cases.
Top Questions on Hydrogen
For hydrogen-like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]Consider the following data:
- Heat of formation of \( CO_2(g) \) = -393.5 kJ mol\(^{-1}\)
- Heat of formation of \( H_2O(l) \) = -286.0 kJ mol\(^{-1}\)
- Heat of combustion of benzene = -3267.0 kJ mol\(^{-1}\)
The heat of formation of benzene is ……… kJ mol\(^{-1}\) (Nearest integer).Which of the following is/are correct with respect to the energy of atomic orbitals of a hydrogen atom?
(A) \( 1s<2s<2p<3d<4s \)
(B) \( 1s<2s = 2p<3s = 3p \)
(C) \( 1s<2s<2p<3s<3p \)
(D) \( 1s<2s<4s<3d \)
Choose the correct answer from the options given below:- The ratio of magnitude of potential energy and kinetic energy for \(5^{th}\) excited state of hydrogen atom is
- If wavelength of the first line of the Paschen series of hydrogen atom is _____ nm, then the wavelength of the second line of this series is nm (Nearest integer)
Questions Asked in JEE Main exam
The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is:
- JEE Main - 2025
- Binomial theorem
- The value of current \( I \) in the electrical circuit as given below, when the potential at \( A \) is equal to the potential at \( B \), will be ________________________ A.
- JEE Main - 2025
- Electrical Circuits
Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.
- JEE Main - 2025
- Current electricity
If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:
- JEE Main - 2025
- Trigonometric Equations
- If \( \int \left( x \sin^{-1} x + \sin^{-1} x (1 - x^2)^{3/2} + \frac{x}{1 - x^2} \right) dx = g(x) + C \), where C is the constant of integration, then \( g\left(\frac{1}{2}\right) \) equals:
- JEE Main - 2025
- Integration by Parts