A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50°C. The gas is now heated to double its temperature on the Celsius scale. The modified pressure is ____ Pa .

Solution

Physics sir · 4 steps

Double the Celsius reading first, then convert both temperatures to kelvin before taking any ratio.

1. Fixed volume. The cylinder is closed, so the volume and the amount of gas do not change. From PV = nRT, the pressure is then directly proportional to the absolute temperature.

   P₂/P₁ = T₂/T₁

2. Convert to kelvin. Doubling 50°C on the Celsius scale gives 100°C. In kelvin, T₁ = 50 + 273 = 323 K and T₂ = 100 + 273 = 373 K.
3. Put in numbers. P₁ = 3.23 kPa = 3230 Pa, so P₂ = 3230 × 373/323 = 10 × 373 Pa.
4. So. The modified pressure is P₂ = 3730 Pa, so the answer is 3730.

The common slip: 6460. Doubling the pressure along with the Celsius temperature gives 6460, but the pressure follows the kelvin temperature, which only goes from 323 K to 373 K.

The idea to keep. Gas laws only work with absolute temperature. Doubling a Celsius reading does not double the kelvin temperature, so always convert to kelvin before taking ratios.

Answer from the NTA final answer key. Solution by PrepWiser.