Import Question JSON

Current Question (ID: 19718)

Question:

$\text{When heat } Q \text{ is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by } \Delta T. \text{ The heat required to produce the same change in temperature, at a constant pressure is:}$

Options:

1. $\frac{7}{5}Q$
2. $\frac{3}{2}Q$
3. $\frac{2}{3}Q$
4. $\frac{5}{3}Q$

Solution:

$\text{Hint: } Q = mC\Delta T$ $Q = mC_vdT$ $Q^1 = mC_pdT$ $\frac{Q_1}{Q} = \frac{C_p}{C_v} = \gamma = \frac{7}{5}$

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
}