Import Question JSON

Current Question (ID: 11026)

Question:

$\text{An ideal gas goes from } A \text{ to } B \text{ via two processes, I and II, as shown. If } \Delta U_1 \text{ and } \Delta U_2 \text{ are the changes in internal energies in processes I and II, respectively, } (P : \text{pressure}, V : \text{volume}) \text{ then:}$

Options:

1. $\Delta U_1 > \Delta U_2$
2. $\Delta U_1 < \Delta U_2$
3. $\Delta U_1 = \Delta U_2$ (Correct)
4. $\Delta U_1 \leq \Delta U_2$

Solution:

$\text{Hint: The change in internal energy depends only on initial and final states.}$ $\text{Explanation: The change in internal energy does not depend upon the path followed by the process, it only depends on the initial and final states. For an ideal gas, the internal energy is a state function, which means it depends only on the temperature of the gas. Since both processes I and II start at point } A \text{ and end at point } B\text{, they have the same initial and final temperatures. Since both processes start and end at the same points, the change in internal energy } \Delta U \text{ will be the same for both paths.}$ $\text{Therefore } \Delta U_1 = \Delta U_2$ $\text{Hence, option (3) is the correct answer.}$

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
}