Import Question JSON

Current Question (ID: 19851)

Question:

$\text{A gas has } n \text{ degrees of freedom. The ratio of the specific heat of the gas at constant volume to the specific heat of the gas at constant pressure will be:}$

Options:

1. $\frac{n}{n+2}$
2. $\frac{n+2}{n}$
3. $\frac{n}{2n+2}$
4. $\frac{n}{n-2}$

Solution:

$\text{Hint: } C_V = \frac{nR}{2}$ $\text{Step: Find the ratio of } \frac{C_V}{C_P}. $ $\text{The ratio of the specific heat of the gas at constant pressure to the specific heat of the gas at constant volume is given by:}$ $\gamma = \frac{2}{f} + 1$ $\Rightarrow \gamma = \frac{2+f}{f}$ $\Rightarrow \frac{C_V}{C_P} = \frac{1}{\gamma} = \left( \frac{n}{n+2} \right)$ $\text{Hence, option (1) is the correct answer.}$

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
}