Import Question JSON

Current Question (ID: 11135)

Question:

$\text{Given below are two statements:}$ \\ \\ $\text{Assertion (A): If a gas container in motion is suddenly stopped, the temperature of the gas rises.}$ \\ $\text{Reason (R): The kinetic energy of ordered mechanical motion is converted into the kinetic energy of random motion of gas molecules.}$

Options:

1. $\text{Both (A) and (R) are true and (R) is the correct explanation of (A).}$ (Correct)
2. $\text{Both (A) and (R) are true but (R) is not the correct explanation of (A).}$
3. $\text{(A) is true but (R) is false.}$
4. $\text{Both (A) and (R) are false.}$

Solution:

$\text{Assertion (A) is true. When a gas container in motion is suddenly stopped, the kinetic energy of the ordered motion of the entire gas system is converted into the internal energy of the gas. This internal energy manifests as the random kinetic energy of the gas molecules. As the temperature of a gas is a measure of the average random kinetic energy of its molecules, an increase in this energy leads to a rise in temperature.}$ \\ \\ $\text{Reason (R) is also true. The macroscopic kinetic energy of the container, which is an ordered motion of all the gas molecules in the same direction, is transformed into the microscopic, random motion of the individual gas molecules upon the container's sudden stop. This conversion is the fundamental reason for the temperature increase described in the assertion.}$ \\ \\ $\text{Since Reason (R) accurately explains why Assertion (A) occurs, both statements are true and R is the correct explanation for A. Therefore, option 1 is the correct choice.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}