Import Question JSON

Current Question (ID: 11177)

Question:

$\text{A cylinder of fixed capacity 44.8 litres contains helium gas at standard temperature and pressure. What is the amount of heat needed to raise the temperature of the gas in the cylinder by }15.0^\circ\text{C}? (R = 8.31\text{ J mol}^{-1}\text{K}^{-1})$

Options:

1. $379\text{ J}$
2. $357\text{ J}$
3. $457\text{ J}$
4. $374\text{ J}$ (Correct)

Solution:

$\text{Hint: The volume of the gas remains constant.}$ $\text{Step 1: Find the no. of moles of the gas.}$ $\text{At standard temperature and the pressure, the molar volume of the gas = 22.4 litres}$ $\text{No. of moles of the gas} = \frac{44.8}{22.4} = 2\text{ moles}$ $\text{Step 2: Find the heat required to raise the temperature of the gas.}$ $\text{For a monatomic gas, molar specific heat at constant volume, }C_V = \frac{3}{2}R$ $\text{Since the volume of the cylinder is fixed,}$ $\text{Heat required} = nC_V \Delta T$ $= 2 \times 1.5R \times 15.0 = 45R$ $= 45 \times 8.31 = 374\text{ J}$

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
}