Import Question JSON

Current Question (ID: 11064)

Question:

$\text{The degree of freedom per molecule for a gas on average is 8. If the gas performs 100 J of work when it expands under constant pressure, then the amount of heat absorbed by the gas is:}$

Options:

1. $\text{500 J}$ (Correct)
2. $\text{600 J}$
3. $\text{20 J}$
4. $\text{400 J}$

Solution:

$\text{Hint: Find the adiabatic index of the gas}$ $\text{Step 1:}$ $\gamma = 1 + \frac{2}{f}$ $= 1 + \frac{2}{8} = 1.25$ $\text{Step 2: Use formula for work}$ $W = P \Delta V = nR \Delta T = 100$ $\text{Step 3: Use formula for heat}$ $C_p = \frac{\gamma R}{\gamma - 1}$ $= 5R$ $Q = nC_p \Delta T = (nR \Delta T)5 = 500 \text{ J}$

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
}