Import Question JSON

Current Question (ID: 11032)

Question:

$\text{If 3 moles of a monoatomic gas do 150 J of work when it expands isobarically, then a change in its internal energy will be:}$

Options:

1. $100 \text{ J}$
2. $225 \text{ J}$ (Correct)
3. $400 \text{ J}$
4. $450 \text{ J}$

Solution:

$\text{For an isobaric process:}$ $W = nR\Delta T$ $\Delta U = nC_V \Delta T$ $\text{For a monoatomic gas:}$ $C_V = \frac{R}{\gamma - 1} = \frac{3R}{2}$ $\text{Given: } n = 3 \text{ moles, } W = 150 \text{ J}$ $\text{From } W = nR\Delta T \text{, we can find:}$ $\Delta T = \frac{W}{nR} = \frac{150}{3R}$ $\text{Therefore:}$ $\Delta U = nC_V \Delta T = \frac{n \times 3R}{2} \Delta T = \frac{3W}{2} = \frac{3 \times 150}{2} = 225 \text{ J}$

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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
}