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Current Question (ID: 8240)

Question:
$\text{What is a necessary condition for an adiabatic process to occur?}$
Options:
  • 1. $\Delta T = 0$
  • 2. $\Delta P = 0$
  • 3. $q = 0$
  • 4. $w = 0$
Solution:
$\textbf{Hint:} \text{Process that occurs without transferring heat between the thermodynamic system and its environment.}$\n\n$\text{Adiabatic refers to a process in which no heat is transferred into or out of a system, and the change in internal energy is only done by work.}$\n\n$\text{A system is said to be under adiabatic conditions if there is no exchange of heat between the system and its surroundings. Hence, under adiabatic conditions, } q = 0.$\n\n$\bullet \, \Delta T = 0: \text{This indicates that there is no change in temperature. However, in an adiabatic process, temperature can change as long as there is no heat exchange with the surroundings. Therefore, this statement is not true for all adiabatic processes.}$\n\n$\bullet \, \Delta P = 0: \text{This means that there is no change in pressure. An adiabatic process can occur with varying pressure, especially in processes involving gases. Hence, this condition is not necessary for an adiabatic process.}$\n\n$\bullet \, q = 0: \text{This is the defining characteristic of an adiabatic process. In an adiabatic process, there is no heat transfer } (q) \text{ between the system and its surroundings. The system can do work or have work done on it, leading to changes in internal energy, but no heat is exchanged.}$\n\n$\bullet \, w = 0: \text{This implies that no work is done. In an adiabatic process, work can still be done on or by the system, as long as there is no heat exchange. Therefore, this condition is not necessary for an adiabatic process.}$\n\n$\text{Therefore, option (3) is correct.}$

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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
}