Import Question JSON

Current Question (ID: 11173)

Question:

$\text{For hydrogen gas, the difference between molar specific heats is given by: } C_P - C_V = a \text{, and for oxygen gas, } C_P - C_V = b \text{. Here, } C_P \text{ and } C_V \text{ are molar specific heats expressed in } \text{J mol}^{-1}\text{K}^{-1} \text{. What is the relationship between } a \text{ and } b\text{?}$

Options:

1. $a = 16b$
2. $b = 16a$
3. $a = 4b$
4. $a = b$ (Correct)

Solution:

$\text{Hint: } C_P - C_V = R$ $\text{Step: Find the relation between } a \text{ and } b$ $\text{The relation between specific heats per unit mass is given by: } C_P - C_V = \frac{R}{M_0}$ $\text{The difference between molar-specific heats } C_P - C_V \text{ does not depend on the gas type (as long as the gas is ideal) because this difference is always equal to } R\text{.}$ $\text{For both hydrogen (}\text{H}_2\text{) and oxygen (}\text{O}_2\text{):}$ $a = R \text{ and } b = R$ $\text{Thus, } a = b$ $\text{Hence, option (4) is the correct answer.}$

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
}