Import Question JSON

Current Question (ID: 11042)

Question:

$\text{The variation of molar heat capacity at constant volume } C_V \text{ with temperature T for a monatomic gas is:}$

Options:

1. $\text{Graph showing } C_V \text{ increasing with T in a curved upward manner}$
2. $\text{Graph showing } C_V \text{ increasing with T in a curved upward manner (steeper)}$
3. $\text{Graph showing } C_V \text{ constant with respect to T (horizontal line)}$ (Correct)
4. $\text{Graph showing } C_V \text{ decreasing with T in a curved downward manner}$

Solution:

$\text{Since, } C_V = \left(\frac{dU}{dT}\right)_V = \frac{f}{2}R$ $\text{Hence, } C_V \text{ does not depend upon T.}$ $\text{For a monatomic gas, the molar heat capacity at constant volume is constant and equal to } \frac{3}{2}R \text{, which is independent of temperature. This corresponds to option 3, showing a horizontal line indicating that } C_V \text{ remains constant with temperature.}$

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
}