Import Question JSON

Current Question (ID: 11040)

Question:

$\text{A monatomic gas is supplied with the heat } Q \text{ very slowly, keeping the pressure constant. The work done by the gas will be:}$

Options:

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

Solution:

$\text{From the first law of thermodynamics:}$ $\Delta Q = \Delta U + \Delta W \Rightarrow \Delta W = (\Delta Q)_p - \Delta U = (\Delta Q)_p \left[1 - \frac{(\Delta Q)_V}{(\Delta Q)_p}\right]$ $= (\Delta Q)_p \left[1 - \frac{C_V}{C_p}\right] = Q \left[1 - \frac{3}{5}\right] = \frac{2}{5}Q$ $\text{Since } (\Delta Q)_p = Q \text{ and } \gamma = \frac{5}{3} \text{ for monatomic gas}$ $\text{For a monatomic ideal gas, } C_V = \frac{3}{2}R \text{ and } C_p = \frac{5}{2}R\text{, so } \frac{C_V}{C_p} = \frac{3}{5}\text{. Therefore, the work done by the gas is } \frac{2}{5}Q\text{.}$

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
}