Import Question JSON

Current Question (ID: 11007)

Question:

$\text{In isothermal expansion, the pressure is determined by:}$

Options:

1. $\text{Temperature only}$
2. $\text{Compressibility only}$ (Correct)
3. $\text{Both temperature and compressibility}$
4. $\text{None of these}$

Solution:

$\text{Isothermal expansion is a process where the temperature of the system remains constant. According to Boyle's Law, for a fixed mass of gas at a constant temperature, the pressure is inversely proportional to the volume. However, the question asks what determines the pressure, not the relationship between pressure and volume. Compressibility is a measure of the change in volume of a substance under pressure. It is defined as:}$ \n\n $\kappa = -\frac{1}{V}(\frac{\partial V}{\partial P})_T$ \n\n $\text{This is the isothermal compressibility. From this equation, we can see that compressibility is a function of pressure (and temperature). Thus, pressure is directly related to compressibility.}$ \n\n $\text{Pressure is the inverse of compressibility. Compressibility describes how much the volume changes when pressure is applied, so a substance with high compressibility will have a low pressure, and vice versa. Therefore, pressure is determined by the compressibility of the gas.}$ \n\n $\text{The correct option is 2.}$

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
}