Import Question JSON

Current Question (ID: 19703)

Question:

$\text{An ideal gas undergoes a thermodynamic process following the relation } PT^2 = \text{ constant. Assuming symbols have their usual meaning, then the volume expansion coefficient of the gas is equal to:}$

Options:

1. $\frac{2}{T^3}$
2. $\frac{3}{T}$
3. $\frac{1}{2T}$
4. $\frac{1}{T}$

Solution:

$\text{Volume expansion coefficient} = V \times \left( \frac{dV}{dT} \right)$ $\text{So,}$ $PT^2 = \text{constant}$ $\frac{T^3}{V} = \text{constant}$ $\frac{dV}{dT} = C \times 3T^2$ $\frac{1}{V} \times \frac{dV}{dT} = \frac{3T^2}{T^3} = \frac{3}{T}$

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
}