Import Question JSON

Current Question (ID: 11140)

Question:

$\text{When an ideal gas is compressed adiabatically, its temperature rises: the molecules on an average have more kinetic energy than before. The kinetic energy increases:}$

Options:

1. $\text{because of collisions with moving parts of the wall only.}$ (Correct)
2. $\text{because of collisions with the entire wall.}$
3. $\text{because the molecules get accelerated in their motion inside the volume.}$
4. $\text{because of the redistribution of energy amongst the molecules.}$

Solution:

$\text{When an ideal gas is compressed adiabatically, there is work done on the gas by the moving piston or wall. This work is converted into the internal energy of the gas, which is directly proportional to the average kinetic energy of the gas molecules. The molecules gain kinetic energy from the moving wall during collisions. Since the wall is moving inward (compressing the gas), the molecules collide with a moving surface and rebound with a higher velocity, thereby increasing their kinetic energy. The increase in kinetic energy is due to the work done by the moving wall. Therefore, the kinetic energy increases because of collisions with moving parts of the wall. This corresponds to option 1.}$

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
}