Import Question JSON

Current Question (ID: 11019)

Question:

$\text{In an adiabatic process, the graph for work done versus change of temperature } \Delta T \text{ will be:}$

Options:

1. $\text{A hyperbolic curve with } W \text{ decreasing as } \Delta T \text{ increases}$
2. $\text{A horizontal line showing } W \text{ is independent of } \Delta T$
3. $\text{A straight line passing through origin with positive slope}$ (Correct)
4. $\text{A straight line not passing through origin with positive slope}$

Solution:

$\text{Work done in an adiabatic process is given by:}$ $W = \left(\frac{R}{\gamma-1}\right)(T_2 - T_1)$ $\text{Hence, } W \propto \Delta T$ $\text{This shows that work done is directly proportional to the change in temperature.}$ $\text{Since } W = k \cdot \Delta T \text{ where } k = \frac{R}{\gamma-1} \text{ is a constant, the graph will be a straight line passing through the origin with positive slope.}$ $\text{Therefore, option (3) is the correct answer.}$

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
}