Import Question JSON

Current Question (ID: 19677)

Question:

$\text{Three different processes that can occur in an ideal monoatomic gas are shown in the } P \text{ vs } V \text{ diagram.}$ $\text{The paths are labelled as } A \rightarrow B, A \rightarrow C \text{ and } A \rightarrow D.$ $\text{The change in internal energies during these processes are taken as } E_{AB}, E_{AC} \text{ and } E_{AD}$ $\text{and the work done as } W_{AB}, W_{AC} \text{ and } W_{AD}. \text{ The correct relation between these parameters are:}$

Options:

1. $E_{AB} = E_{AC} = E_{AD}, W_{AB} > 0, W_{AC} = 0, W_{AD} < 0$
2. $E_{AB} < E_{AC} < E_{AD}, W_{AB} > 0, W_{AC} > W_{AD}$
3. $E_{AB} = E_{AC} < E_{AD}, W_{AB} > 0, W_{AC} = 0, W_{AD} < 0$
4. $E_{AB} > E_{AC} > E_{AD}, W_{AB} < W_{AC} < W_{AD}$

Solution:

$\Delta U = \frac{n f R}{2} (T_f - T_i), W = P \Delta V.$ $\Delta U = n C_V \Delta T = \text{same}$ $AB \rightarrow \text{volume is increasing} \Rightarrow W > 0$ $AD \rightarrow \text{volume is decreasing} \Rightarrow W < 0$ $AC \rightarrow \text{volume is constant} \Rightarrow W = 0$

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
}