Import Question JSON

Current Question (ID: 8245)

Question:

$\text{In an adiabatic process, no transfer of heat takes place between the system and its surroundings. The correct option for free expansion of an ideal gas under adiabatic condition from the following is:}$

Options:

1. $q = 0, \, \Delta T \neq 0, \, W = 0$
2. $q \neq 0, \, \Delta T = 0, \, W = 0$
3. $q = 0, \, \Delta T = 0, \, W = 0$
4. $q = 0, \, \Delta T = 0, \, W \neq 0$

Solution:

\textbf{Hint:} \text{For an adiabatic process, } dq = 0 \text{For free expansion, } W = 0 \text{and Adiabatic process, } q = 0 \Delta U = q + W = 0, \text{ this means that internal energy remains constant.} \text{Therefore, } \Delta T = 0 \text{ In the ideal gas, there is no intermolecular attraction.} \text{Hence, when such a gas expands under adiabatic conditions into a vacuum, no heat is absorbed or evolved since no external work is done to separate the molecules.} \text{For free expansion of an ideal gas under adiabatic conditions:} \text{• } q = 0 \text{ (adiabatic process - no heat transfer)} \text{• } W = 0 \text{ (free expansion - no work done against external pressure)} \text{• } \Delta T = 0 \text{ (since } \Delta U = q + W = 0 + 0 = 0 \text{, and for ideal gas } \Delta U = nC_v\Delta T \text{, so } \Delta T = 0\text{)} \text{Therefore, option (3) is correct.}

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
}