Import Question JSON

Current Question (ID: 11018)

Question:
$\text{Two identical samples of a gas are allowed to expand, (i) isothermally and (ii) adiabatically. The work done will be:}$
Options:
  • 1. $\text{more in the isothermal process.}$ (Correct)
  • 2. $\text{more in the adiabatic process.}$
  • 3. $\text{equal in both processes.}$
  • 4. $\text{none of the above.}$
Solution:
$\text{Hint: The amount of work done in an adiabatic expansion is less than in an isothermal expansion.}$ $\text{Explanation: In a thermodynamic process,}$ $\text{The work done = The area covered by P-V diagram with V-axis}$ $\text{From the P-V diagram, it is clear that } (\text{Area})_{iso} > (\text{Area})_{adi}$ $\Rightarrow W_{iso} > W_{adi}$ $\text{When a gas expands isothermally, the temperature remains constant, meaning the internal energy of the gas does not change. In this case, all the energy used in the expansion process goes into doing work on the surroundings.}$ $\text{In an adiabatic process, there is no heat exchange with the surroundings. Therefore the gas uses some of its internal energy for expansion, which causes the temperature of the gas to decrease. As a result, the amount of work done in an adiabatic expansion is less than in an isothermal expansion, since part of the internal energy is used to decrease the temperature rather than do external work.}$ $\text{Hence, option (1) is the correct answer.}$

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
}