Import Question JSON

Current Question (ID: 19729)

Question:

$\text{The pressure } P_1 \text{ and density } d_1 \text{ of diatomic gas } \left( \gamma = \frac{7}{5} \right) \text{ change suddenly to } P_2 ( > P_1) \text{ and } d_2 \text{ respectively during an adiabatic process.}$ $\text{The temperature of the gas increases and becomes:}$ $\left( \text{given } \frac{d_2}{d_1} = 32 \right)$

Options:

1. $2 \text{ times its initial temperature.}$
2. $4 \text{ times its initial temperature.}$
3. $6 \text{ times its initial temperature.}$
4. $8 \text{ times its initial temperature.}$

Solution:

$\text{Hint: } PV^\gamma = \text{constant}$

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
}