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The equilibrium constant for the reaction: \[ \text{CaCO}_{3(\text{s})} \rightleftharpoons \text{CaO}_{(\text{s})} + \text{CO}_{2(\text{g})} \] Which of the following statements are correct? (A) \( K \) is independent of the initial amount of \(\text{CaCO}_{3}\) (B) At a given temperature, \( K \) is independent of the pressure of \(\text{CO}_{2}\) (C) \( \Delta H \) is dependent on the catalyst (D) \( \Delta H \) depends on temperature Show Answer The correct options are: (A), (B), and (D) . Explanation: For the equilibrium \[ \text{CaCO}_{3(\text{s})} \rightleftharpoons \text{CaO}_{(\text{s})} + \text{CO}_{2(\text{g})}, \] the equilibrium constant \(K\) is independent of the initial amount of \(\text{CaCO}_{3}\). At a given temperature, \(K\) is independent of the pressure of \(\text{CO}_{2}\), and \(\Delta H\) is independent of...

15 practice questions of KTG and Thermodynamics for JEE Advanced 15 Practice questions on KTG and Thermodynamics  for JEE Advanced Are you ready to challenge yourself with some of the toughest Kinetic Theory of Gases (KTG) and Thermodynamics problems? Here are 15 carefully selected advanced-level questions to help you gear up for JEE Advanced. Make sure you understand the concepts from our KTG and Thermodynamics notes before attempting these questions. Question 1: Calculate the number of degrees of freedom for a diatomic gas at room temperature and find the total internal energy of 1 mole of the gas at 300 K. Assume ideal gas behavior. Solution: A diatomic gas has 5 degrees of freedom (3 translational and 2 rotational) at room temperature. Total Internal Energy = \( U = \frac{5}{2} nRT \) Substituting the values: \( U = \frac{5}{2} \times 1 \times 8.314 \times 300 = 6235....

Kinetic Theory of Gases and Thermodynamics - JEE Advanced Notes Kinetic Theory of Gases and Thermodynamics - Detailed Notes Introduction Kinetic Theory of Gases (KTG) and Thermodynamics are fundamental topics for JEE aspirants. Understanding the microscopic behavior of gas molecules and the laws governing energy, heat, and work is essential. In this post, we will cover every concept in detail with examples to help you master these topics up to the JEE Advanced level. Kinetic Theory of Gases (KTG) Basic Assumptions of Kinetic Theory Gases consist of a large number of molecules in random motion. Molecules of a gas are point masses with no internal structure. Collisions between molecules are perfectly elastic. No intermolecular forces act between the molecules except during collisions. Key Formulas in KTG Average Kinetic Energy: \( \frac{3}{2} k_B T \) Where \( k_B \) is the Boltzmann...

Advanced Applications of Derivatives for JEE 1. Rate of Change Rate of change measures how one quantity changes with respect to another. If \( y = f(x) \), then the rate of change is \( f'(x) \). Example: \( f(x) = 3x^2 \) gives \( f'(x) = 6x \). 2. Monotonicity If \( f'(x) > 0 \), the function is increasing; if \( f'(x) < 0 \), it is decreasing. Advanced Applications of Derivatives for JEE 1. Newton-Leibniz Formula The Newton-Leibniz formula relates the integral of a function to its antiderivative. It states that if \( F(x) \) is the antiderivative of \( f(x) \), then: \[ \int_a^b f(x)\,dx = F(b) - F(a) \] Example: Evaluate \( \int_1^3 2x \, dx \): \[ \int_1^3 2x \, dx = x^2 \Big|_1^3 = 9 - 1 = 8 \] 2. Jansen's Inequality Jensen's inequality applies to convex functions, stating that for any convex function \( f \) and real numbers \( x_1, x_2, ...

JEE Advanced 2024 - Question 1 Question: An extended object is placed at point O, 10 cm in front of a convex lens L₁, and a concave lens L₂ is placed 10 cm behind it. The radii of curvature of all the curved surfaces in both lenses are 20 cm. The refractive index of both lenses is 1.5. The total magnification of this lens system is: (a) 0.4 (b) 0.8 (c) 1.3 (d) 1.6 Check Answer Solution: Using the lens maker's formula: \[ \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] The correct answer is Option B (0.8). Relevant Posts:

Dimensionless Quantity in Physics A dimensionless quantity is constructed in terms of electronic charge \( e \), permittivity of free space \( \varepsilon_0 \), Planck’s constant \( h \), and the speed of light \( c \). If the dimensionless quantity is written as \( e^{\alpha} \varepsilon_0^{\beta} h^{\gamma} c^{\delta} \) and \( n \) is a non-zero integer, then (\( \alpha, \beta, \gamma, \delta \)) is given by: Select the correct option: (A) \( (2n, -n, -n, -n) \) (B) \( (n, -n, -2n, -n) \) (C) \( (n, -n, -n, -2n) \) (D) \( (2n, -n, -2n, -2n) \) Check Answer The correct answer is (A) \( (2n, -n, -n, -n) \) . For the quantity to be dimensionless: For the quantity to be dimensionless: $$ e^{\alpha} \varepsilon_0^{\beta} h^{\gamma} c^{\delta} = M^0L^0T^0A^0 $$ Equating the dimensions: $$ (AT)^{\alpha} \left(M^{-1}L^{-3}T^{4}A^{2}\right)^{\beta} \left(M^1L^2T^{-1}\right)^{\gamma} \lef...

Class 12 Chemistry: Solutions - StudyBeacon Class 12 Chemistry: Solutions - Revision Notes Introduction The chapter "Solutions" in Class 12 Chemistry covers essential concepts like types of solutions, concentration terms, Raoult's Law, colligative properties, and more. Understanding these concepts is crucial for both board exams and competitive exams like JEE and NEET. In this post, we'll dive deep into the various topics and provide detailed solutions with all the necessary formulae. Types of Solutions A solution is a homogeneous mixture of two or more substances. The substance present in a smaller amount is called the solute , and the substance present in a larger amount is the solvent . Types Based on Solvent and Solute: Solid in Liquid Solutions: Example - Sugar in water. Gas in Liquid Solutions: Example - Carbon dioxide in water (soda water). Liquid in Liquid Solutions: Example - Alcohol in ...

Comprehensive Revision Guide on Relations and Functions for Class 12 Welcome back to StudyBeacon's Revision Series ! Today, we dive into one of the most essential chapters of Class 12 Mathematics— Relations and Functions . This topic is the backbone for various concepts in calculus and algebra. In this guide, we’ll explore the various types of relations and functions, break down their properties, and tackle some challenging questions to sharpen your skills for exams like JEE Advanced. Let's get started! Understanding Relations and Functions To put it simply, a relation is a rule that connects elements from one set to another. A function is a special type of relation where each input has a unique output. Let's break this down further. 1. Types of Relations Relations help us understand how two sets of information are interconnected. Here are the various types: Empty Relation: If none of the elements of set A are related to...

Mastering Gas Dynamics: The Secrets of Mean Free Path and Kinetic Energy Hey there, science enthusiasts! Today, we’re diving deep into the fascinating world of gas molecules. We have a question that explores two core concepts of gas dynamics: the mean free path and the kinetic energy of gas molecules. Understanding these can really sharpen your problem-solving skills, especially if you're prepping for exams like JEE, NEET, or the Olympiads. Let’s break it down step-by-step! The Question at Hand Consider these two statements: Statement (I): The mean free path of gas molecules is inversely proportional to the square of the molecular diameter. Statement (II): The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas. Which of the following options is correct? Statement I is false but Statement II is true. Statement I is true but Statement II is false. Both Statement I and Statement II are false. Both S...

P-Block Elements Revision - JEE Advanced Level The P-block elements in the periodic table consist of elements in groups 13 to 18. These elements show a wide range of properties due to the different types of elements present (metals, non-metals, and metalloids). Understanding the unique characteristics, trends, and reactions of P-block elements is crucial for JEE Advanced preparation. For a revision of the periodic table trends, check our Periodic Table Revision Series . 1. Key Properties and Trends of P-Block Elements P-block elements exhibit varied properties based on their group and period position. Some important trends include: Property Group 13 Group 14 Group 15 Group 16 Group 17 Group 18 Metallic Character Increases down the group Decreases down the group Decreases down the group Increases down the group Decreases down the group ...

S-Block Elements Revision - JEE Advanced Level The S-block elements of the periodic table, consisting of Group 1 (alkali metals) and Group 2 (alkaline earth metals), are characterized by their distinct physical and chemical properties. Understanding their properties, trends, and reactions is crucial for JEE Advanced preparation. For a revision of the periodic table trends, check our Periodic Table Revision Series . 1. Key Properties and Trends of S-Block Elements S-block elements exhibit properties such as low ionization energies, high reactivity, and formation of ionic compounds. Some important trends include: Property Group 1 (Alkali Metals) Group 2 (Alkaline Earth Metals) Atomic Radius Increases down the group Increases down the group Ionization Energy Decreases down the group Decreases down the group Electronegativity Decreases do...

Periodic Table Revision for JEE The periodic table is one of the most fundamental concepts in chemistry, especially for students preparing for competitive exams like JEE. It provides a structured way to understand the properties, trends, and behaviors of elements. This article will help you revise the periodic table for JEE with a focus on key trends, important groups, and exam-centric insights. 1. Understanding the Periodic Table The periodic table is arranged in periods and groups, where elements are placed based on their atomic number, electronic configuration, and recurring chemical properties. Each element has a unique position that reflects its properties. Knowing these properties is crucial for solving JEE questions effectively. Quick Fact: The periodic table consists of 18 groups (vertical columns) and 7 periods (horizontal rows). Elements are categorized into metals, non-metals, metalloids, and noble gases. 2. Key Trends to Remember ...

Work, Power, and Energy Revision - JEE Advanced Level Work, Power, and Energy are fundamental concepts in mechanics. Understanding these concepts is crucial for solving problems related to energy conservation, work done by forces, and power output. In this post, we will cover the key formulas, interactive examples, and simulations to help you master these concepts. 1. Key Formulas Below is a table summarizing the important formulas related to work, power, and energy: Concept Formula Description Work Done \[ W = F \cdot d \cdot \cos(\theta) \] Work done is the product of force, displacement, and the cosine of the angle between them. Kinetic Energy \[ KE = \frac{1}{2} mv^2 \] Kinetic energy is the energy of motion, dependent on mass and velocity. Potential Energy \[ PE = mgh \] Potential energy is the energy stored due to an object...