Import Question JSON

Current Question (ID: 19744)

Question:

$\text{A total of } 48 \text{ J heat is given to one mole of helium kept in a cylinder.}$ $\text{The temperature of helium increases by } 2^\circ \text{C. The work done by the gas is:}$ $\text{(Given: } R = 8.31 \text{ Jk}^{-1} \text{mol}^{-1})$

Options:

1. $48 \text{ J}$
2. $23.1 \text{ J}$
3. $24.9 \text{ J}$
4. $72.9 \text{ J}$

Solution:

$\text{For a monoatomic gas, } f = 3$ $\Delta Q = 48 \text{ J}$ $n = 1$ $\Delta T = 2^\circ \text{C}$ $W = \frac{f}{2} n R \Delta T = \frac{3}{2} \times 1 \times 8.31 \times 2 = 24.93 \text{ J}$

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
}