Import Question JSON

Current Question (ID: 11052)

Question:

$\text{An ideal gas goes from state A to state B via three different processes, as indicated in the } P\text{-}V \text{ diagram. If } Q_1, Q_2, Q_3 \text{ indicates the heat absorbed by the gas along the three processes and } \Delta U_1, \Delta U_2, \Delta U_3 \text{ indicates the change in internal energy along the three processes respectively, then:}$

Options:

1. $Q_1 > Q_2 > Q_3 \text{ and } \Delta U_1 = \Delta U_2 = \Delta U_3$ (Correct)
2. $Q_3 > Q_2 > Q_1 \text{ and } \Delta U_1 = \Delta U_2 = \Delta U_3$
3. $Q_1 = Q_2 = Q_3 \text{ and } \Delta U_1 > \Delta U_2 > \Delta U_3$
4. $Q_3 > Q_2 > Q_1 \text{ and } \Delta U_1 > \Delta U_2 > \Delta U_3$

Solution:

$\text{For all process 1, 2 and 3}$ $\Delta U = U_B - U_A$ $\text{so, } \Delta U_1 = \Delta U_2 = \Delta U_3$ $\text{Now, } \Delta Q = \Delta U + \Delta W$ $\text{Now, } \Delta W = \text{work done by the gas}$ $\text{so, } \Delta Q_1 > \Delta Q_2 > \Delta Q_3$

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
}