Import Question JSON

Current Question (ID: 11055)

Question:

$\text{The work done by an ideal diatomic gas in its sudden expansion is 20 J. The change in the internal energy of the gas will be:}$

Options:

1. $20 \text{ J}$
2. $0 \text{ J}$
3. $-20 \text{ J}$ (Correct)
4. $-15 \text{ J}$

Solution:

$\text{Hint: For a sudden (adiabatic) expansion, no heat is exchanged with the surroundings (Q = 0).}$ $\text{Explanation: Using the first law of thermodynamics:}$ $\Delta U = Q - W$ $\text{For an adiabatic process, Q = 0, so:}$ $\Delta U = 0 - W = -W$ $\text{Since work done BY the gas is positive (W = +20 J), the change in internal energy is:}$ $\Delta U = -20 \text{ J}$ $\text{This means the internal energy decreases by 20 J as the gas does work during expansion.}$

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
}