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Current Question (ID: 11116)

Question:

$\text{How does the temperature change when the state of an ideal gas is changed according to the process shown in the figure?}$

Options:

1. $\text{temperature increases continuously.}$
2. $\text{temperature decreases continuously.}$
3. $\text{temperature first increases and then decreases.}$ (Correct)
4. $\text{temperature first decreases and then increases.}$

Solution:

$\text{For a fixed amount of an ideal gas, the product of pressure and volume, } PV \text{, is directly proportional to the absolute temperature, } T \text{. The ideal gas law is given by } PV = nRT \text{, where } n \text{ is the number of moles and } R \text{ is the ideal gas constant. The relationship } PV \propto T \text{ implies that for a given temperature, the product } PV \text{ is constant. A graph of } P \text{ versus } V \text{ for a constant temperature process is a hyperbola, known as an isotherm. The isotherms for higher temperatures are further away from the origin. By drawing isotherms on the given graph, we can trace the path from point 'a' to 'b'. The process starts at point 'a' and moves along a curved path. We can see that the path first crosses isotherms of increasing temperature, reaching a maximum temperature somewhere near the top of the curve, and then crosses isotherms of decreasing temperature, ending at point 'b' on an isotherm with a lower temperature than the maximum. Therefore, the temperature first increases and then decreases during this process.}$

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
}