Import Question JSON

Current Question (ID: 11175)

Question:

$\text{The value of } C_P - C_v = 1.00R \text{ for a gas in state A and } C_P - C_v = 1.06R \text{ in another state B. If } P_A \text{ and } P_B \text{ denote the pressure and } T_A \text{ and } T_B \text{ denote the temperatures in the two states, then:}$

Options:

1. $P_A = P_B; T_A > T_B$
2. $P_A > P_B; T_A = T_B$
3. $P_A < P_B; T_A > T_B$ (Correct)
4. $P_A = P_B; T_A < T_B$

Solution:

$\text{For gas A: } C_P - C_v = R \text{. So it is an ideal gas.}$ $\text{For gas B: } C_P - C_v = 1.6R \text{. So it is not ideal gas.}$ $\text{Gas A is more likely to be more ideal at high temperature and low pressure.}$ $\text{So } P_A < P_B \text{ and } T_A > T_B$

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
}