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Current Question (ID: 11092)

Question:
The efficiency of an ideal heat engine is less than 100% because of:
Options:
  • 1. $\text{the presence of friction.}$
  • 2. $\text{the leakage of heat energy.}$
  • 3. $\text{unavailability of the sink at zero kelvin.}$
  • 4. $\text{all of these.}$ (Correct)
Solution:
$\text{Hint: The system can't be perfectly insulating and there are dissipating forces.}$ Explanation: In real engines, friction between moving parts causes energy loss. Although friction doesn't apply to an idealized, perfectly frictionless heat engine, real engines are affected by friction, reducing efficiency. In practice, heat may leak or dissipate from the system due to imperfect insulation. This heat loss lowers the effective amount of energy that can be converted into work, thus lowering the efficiency. This is a fundamental limitation imposed by the second law of thermodynamics. For an ideal heat engine, reaching 100% efficiency would require the cold reservoir (sink) to be at absolute zero (0 K), which is impossible to achieve. This thermodynamic limit applies to both ideal and real heat engines.}$ $\text{The efficiency of an ideal heat engine is less than 100% because of all the given factors. As heat converts into work.}$ $\text{Hence, option (4) is the correct answer.

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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
}