Import Question JSON

Current Question (ID: 11078)

Question:

$\text{Which one of the following is correct for one complete cycle of a thermodynamic process on a gas as shown in the } (P - V) \text{ diagram?}$

Options:

1. $\Delta E_{\text{int}} = 0, Q < 0$ (Correct)
2. $\Delta E_{\text{int}} = 0, Q > 0$
3. $\Delta E_{\text{int}} > 0, Q < 0$
4. $\Delta E_{\text{int}} < 0, Q > 0$

Solution:

$\text{Hint: } \delta Q = \Delta U + \delta W$ $\text{Explanation: For the cyclic process } \Delta E_{\text{int}} = 0$ $\text{For anticlockwise rotation of the process, } \delta W = -\text{ve}$ $\text{From the first law of thermodynamics}$ $Q = \Delta E_{\text{int}} + W$ $Q < 0$ $\text{Hence, option (1) is the correct answer.}$

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
}