Import Question JSON

Current Question (ID: 21041)

Question:

$\text{An ideal gas expands in volume from } 1 \times 10^{-3} \text{ m}^3 \text{ to } 1 \times 10^{-2} \text{ m}^3 \text{ at 300 K against a constant pressure of } 1 \times 10^5 \text{ Nm}^{-2}. \text{ The work done is:}$

Options:

1. $-900 \text{ J}$
2. $-900 \text{ kJ}$
3. $270 \text{ kJ}$
4. $900 \text{ kJ}$

Solution:

$\text{Hint: } W = -P(V_2 - V_1)$ $\text{Step 1:}$ $\text{The formula of work done is as follows:}$ $w = -P \Delta V; = -P(V_2 - V_1)$ $\text{The given values are as follows:}$ $P = 1 \times 10^5 \text{ Nm}^{-2}$ $V_2 = 1 \times 10^{-2} \text{ m}^3$ $V_1 = 1 \times 10^{-3} \text{ m}^3$ $\text{Step 2:}$ $\text{Calculate the work done as follows:}$ $W = -P(V_2 - V_1)$ $= -1 \times 10^5 (1 \times 10^{-2} - 1 \times 10^{-3})$ $W = -900 \text{ Nm}$ $\text{1 Nm is equal to 1 J.}$ $\text{Thus, option one is the correct answer.}$

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
}