Import Question JSON

Current Question (ID: 19668)

Question:

$C_P \text{ and } C_V \text{ are specific heats at constant pressure and constant volume respectively. It is observed that}$ $C_P - C_V = a \text{ for hydrogen gas}$ $C_P - C_V = b \text{ for nitrogen gas}$ $\text{The correct relation between } a \text{ and } b \text{ is:}$

Options:

1. $a = \frac{1}{14}b$
2. $a = b$
3. $a = 14b$
4. $a = 28b$

Solution:

$\text{Hint: } C = MS_g$ $C_p - C_v = R$ $\text{If } C_p \text{ and } C_v \text{ are molar specific heat}$ $\text{But if } C_p \text{ and } C_v \text{ are specific heat i.e. gram specific heat then}$ $C = MS_g$ $S_g = \frac{C}{M}$ $MS_{gp} - MS_{gv} = R$ $S_{gp} - S_{gv} = \frac{R}{M}$ $\frac{R}{2R} = a$ $\frac{R}{28} = b$ $14 = \frac{a}{b}$ $a = 14b$

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
}