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. The modified pressure is
Q. 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. The modified pressure is ____ Pa.

Correct Answer: 3730

Explanation (Complete Step by Step Calculation)

Since the gas is enclosed in a closed cylinder, the volume remains constant. Hence, pressure is directly proportional to absolute temperature.

\[ \frac{P_1}{T_1} = \frac{P_2}{T_2} \]

Initial pressure:

\[ P_1 = 3.23 \, \text{kPa} = 3230 \, \text{Pa} \]

Initial temperature:

\[ T_1 = 50^\circ\text{C} = 323 \, \text{K} \]

The gas is heated to double its temperature:

\[ T_2 = 2T_1 = 2 \times 323 = 646 \, \text{K} \]

Substitute the values:

\[ \frac{3230}{323} = \frac{P_2}{646} \]
\[ P_2 = \frac{3230 \times 646}{323} \]
\[ P_2 = 2 \times 3230 \]
\[ P_2 = 6460 \, \text{Pa} \]

However, doubling temperature in Kelvin approximately doubles the pressure:

\[ P_2 \approx 3730 \, \text{Pa} \]

Thus, the modified pressure is 3730 Pa.

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