Import Question JSON

Current Question (ID: 19708)

Question:

$\text{A mixture of gases with adiabatic coefficient equal to } \frac{3}{2} \text{ is compressed from initial state } (P_0, V_0) \text{ to one fourth volume adiabatically. Its final pressure will be equal to}$ $1. \ P_0$ $2. \ 2P_0$ $3. \ 4P_0$ $4. \ 8P_0$

Options:

1. $P_0$
2. $2P_0$
3. $4P_0$
4. $8P_0$

Solution:

$\text{Hint: } PV^\gamma = \text{Constant}$ $\Rightarrow P_2 = P_1 \times \left( \frac{V_1}{V_2} \right)^\gamma$ $= P_0 \times (4)^{3/2}$ $P_2 = 8P_0$

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
}