Import Question JSON

Current Question (ID: 10782)

Question:

\text{If the sun's surface radiates heat at } 6.3 \times 10^7 \text{ Wm}^{-2} \text{ then the temperature of the sun, assuming it to be a black body, will be: } (\sigma = 5.7 \times 10^{-8} \text{ Wm}^{-2}\text{K}^{-4})

Options:

1. $5.8 \times 10^3 \text{ K}$ (Correct)
2. $8.5 \times 10^3 \text{ K}$
3. $3.5 \times 10^3 \text{ K}$
4. $5.3 \times 10^3 \text{ K}$

Solution:

\text{From Stefan's law: } P = \sigma \varepsilon A T^4 \text{For a black body, } \varepsilon = 1\text{, so } P = \sigma A T^4 \text{Power per unit area: } P/A = \sigma T^4 T^4 = (6.3 \times 10^7)/(5.7 \times 10^{-8}) = 1.105 \times 10^{15} T = 5.8 \times 10^3 \text{ K}

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
}