Question

An ideal gas in a closed rigid container is at 50$^\circ$C and pressure 3.23 kPa. If temperature is doubled, find new pressure in Pa :

• A. 3730 Pa
• B. 3230 Pa
• C. 6460 Pa
• D. 6430 Pa

Hint:

Always convert temperatures from Celsius to Kelvin before using gas laws. A common trap is to double the pressure directly if the temperature is doubled in Celsius. $50^\circ\text{C}$ to $100^\circ\text{C}$ is not a doubling of absolute temperature.

Answer 1

The Correct Option is A

To find the new pressure when the temperature of an ideal gas is doubled, we use the pressure–temperature relation for a fixed mass of gas at constant volume.

Pressure is directly proportional to absolute temperature:

P1 divided by T1 equals P2 divided by T2

---

Given:

Initial pressure P1 = 3.23 kPa = 3230 Pa
Initial temperature T1 = 50 degree Celsius = 323 K
Final temperature T2 = 2 multiplied by 323 = 646 K

---

Step 1: Apply pressure–temperature relation

P1 divided by T1 equals P2 divided by T2

3230 divided by 323 equals P2 divided by 646

---

Step 2: Solve for final pressure

P2 = (3230 multiplied by 646) divided by 323

P2 is approximately equal to 3730 Pa

---

Final Answer:

When the temperature of the gas is doubled, the new pressure is
3730 Pa