Import Question JSON

Current Question (ID: 11034)

Question:

$\text{When an ideal diatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is:}$

Options:

1. $\frac{2}{5}$
2. $\frac{3}{5}$
3. $\frac{3}{7}$
4. $\frac{5}{7}$ (Correct)

Solution:

$\text{Hint: } \Delta U = mC_V\Delta T$ $\text{Step: Find the fraction of the heat energy supplied which increases the internal energy of the gas.}$ $\text{The total heat energy supplied to the gas at constant pressure is given by:}$ $Q = mC_P\Delta T$ $\text{The increase in internal energy of the gas is given by:}$ $\Delta U = mC_V\Delta T$ $\text{The fraction of heat energy that increases the internal energy, we need to calculate the ratio:}$ $\frac{\Delta U}{Q} = \frac{C_V}{C_P}$ $\text{For a diatomic gas: } C_V = \frac{5}{2}R \text{ and } C_P = \frac{7}{2}R$ $\frac{\Delta U}{Q} = \frac{\frac{5}{2}R}{\frac{7}{2}R} = \frac{5}{7}$ $\text{Hence, option (4) is the correct answer.}$

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
}