Import Question JSON

Current Question (ID: 19695)

Question:

$\text{Starting with the same initial conditions, an ideal gas expands from volume } V_1 \text{ to } V_2 \text{ in three different ways. The work done by the gas is } W_1 \text{ if the process is purely isothermal, } W_2 \text{ if the process is purely adiabatic and } W_3 \text{ if the process is purely isobaric. Then,}$

Options:

1. $W_1 < W_2 < W_3$
2. $W_2 < W_3 < W_1$
3. $W_3 < W_1 < W_2$
4. $W_2 < W_1 < W_3$

Solution:

$\text{Hint: Work done = Area under } (P - V) \text{ graph.}$ $\text{Step 1: Draw a diagram.}$ $\text{Step 2: Compare the work done in different processes.}$ $\text{Work done = Area under } (P - V) \text{ graph.}$ $\text{From the graph, we can conclude that;} W_2 < W_1 < W_3$

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
}