Import Question JSON

Current Question (ID: 11082)

Question:

$\text{In a cyclic process, the internal energy of the gas:}$

Options:

1. $\text{increases}$
2. $\text{decreases}$
3. $\text{remains constant}$ (Correct)
4. $\text{becomes zero}$

Solution:

$\text{Hint: The internal energy is a state function.}$ $\text{Explanation: In a cyclic process, the system returns to its initial state at the end of each cycle. Since internal energy is a state function (meaning it depends only on the current state of the system and not on the path taken), the internal energy must be the same at the start and end of each cycle.}$ $\text{Since the system returns to its original state, the internal energy does not change over the course of the cycle, even if there is work done or heat exchanged within the cycle.}$ $\text{Internal energy is a state function.}$ $\text{Note: The internal energy will remain the same and the change in internal energy would be zero.}$ $\text{Hence, option (3) is the correct answer.}$

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
}