Import Question JSON

Current Question (ID: 19888)

Question:

$\text{A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (} 27^\circ \text{C)}.$ $\text{The ratio of specific heat of gases at constant volume respectively is:}$

Options:

1. $\frac{3}{2}$
2. $\frac{5}{2}$
3. $\frac{3}{2} \text{ and } \frac{5}{2}$
4. $\frac{5}{2} \text{ and } \frac{3}{2}$

Solution:

$\text{For a monoatomic gas, } C_V = \frac{3}{2}R.$ $\text{For a diatomic gas (rigid), } C_V = \frac{5}{2}R.$ $\text{Thus, the ratio is } \frac{3}{2} : \frac{5}{2}.$

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
}