Import Question JSON

Current Question (ID: 19659)

Question:

$\text{Read the following statements:}$ $\text{A. When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice.}$ $\text{B. Two bodies P and Q having equal surface areas are maintained at temperature 10}^\circ\text{C and 20}^\circ\text{C. The thermal radiation emitted in a given time by P and Q are in the ratio 1 : 1.15}$ $\text{C. A car engine working between 100 \text{ K and } 400 \text{ K has an efficiency of 75\%}}$ $\text{D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.}$ $\text{Choose the correct answer from the options given below:}$

Options:

1. $\text{A, B, C only}$
2. $\text{A, B only}$
3. $\text{A, C only}$
4. $\text{B, C, D only}$

Solution:

$\text{Statement A is incorrect because the rate of loss of heat is proportional to the temperature difference, not twice.}$ $\text{Statement B is correct as per Stefan-Boltzmann law.}$ $\text{Statement C is incorrect because the efficiency of a Carnot engine is } \eta = 1 - \frac{T_1}{T_2} = 1 - \frac{100}{400} = 0.75 \text{ or 75\%.}$ $\text{Statement D is incorrect because quadrupling the temperature difference would quadruple the rate of heat loss, not double it.}$

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
}