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Current Question (ID: 10813)

Question:

$\text{The rate of heat emission from an ideal black body at temperature T is H. What will be the rate of emission of heat by another body of same size at temperature 2T and emissivity 0.25?}$

Options:

1. $16\text{H}$
2. $4\text{H}$ (Correct)
3. $8\text{H}$
4. $4.5\text{H}$

Solution:

$\text{The rate of heat emission from a body is given by the Stefan-Boltzmann law:}$ $P = e\sigma AT^4$ $\text{For the first body (ideal black body), the emissivity (e) is 1. The initial rate of emission is given as H.}$ $H = (1)\sigma AT^4$ $\text{For the second body, the emissivity is 0.25 and the temperature is 2T. The area A is the same. The new rate of emission, } P' \text{, is:}$ $P' = (0.25)\sigma A(2T)^4$ $P' = 0.25\sigma A(16T^4)$ $P' = 4(\sigma AT^4)$ $\text{Since } H = \sigma AT^4 \text{, we can substitute this into the equation for } P' \text{:}$ $P' = 4H$

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
}