Import Question JSON

Current Question (ID: 19674)

Question:

$\text{A closed vessel contains } 0.1 \text{ mole of a monatomic ideal gas at } 200 \text{ K.}$ $\text{If } 0.05 \text{ mole of the same gas at } 400 \text{ K is added to it, the final}$ $\text{equilibrium temperature (in K) of the gas in the vessel will be closed to:}$

Options:

1. $133$
2. $57$
3. $266$
4. $504$

Solution:

$\text{As work done on gas and heat supplied to the gas are zero,}$ $\text{Total internal energy of gases remain same}$ $u_1 + u_2 = u'_1 + u'_2$ $(0.1)C_v(200) + (0.05)C_v(400) = (0.15)C_vT$ $T = \frac{800}{3}K = 266.67 \text{ K}$

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
}