Import Question JSON

Current Question (ID: 21013)

Question:

$\text{Calculate the amount of heat is absorbed for an ideal gas which expands isothermally from 4 litre to 20 litre against the vacuum.}$

Options:

1. $0$
2. $-50 \text{ kJ}$
3. $50 \text{ kJ}$
4. $-40 \text{ kJ}$

Solution:

$\text{For the isothermal process, } \Delta T \text{ is zero. Hence } \Delta U \text{ is also zero.}$ $\text{For the isothermal process, } -q = W$ $\text{The formula of work done is as follows:}$ $W = -P_{\text{ext}} \Delta V$ $\text{Ideal gas expands isothermally a vacuum. } P_{\text{ext}} \text{ at Vacuum is zero.}$ $\text{Work done against vacuum } = 0$ $\text{As process is isothermal so } \Delta U = 0$ $\Delta U = q + w$ $\text{so } q = 0$ $\text{Hence, option first is the answer.}$

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
}