Gas Laws

Step 1: Using the Ideal Gas Law For an ideal gas, the pressure is given by: where: - is the pressure, - is the molecular mass, - is the number density of molecules, - is the root mean square velocity of gas molecules.

Step 2: Understanding the Effects of Given Changes 1. The rms speed is proportional to the square root of temperature: Since the average speed is doubled, we get: Squaring both sides: Since , the pressure increases 4 times due to this effect. 2. The volume is halved, and from the ideal gas equation: Since temperature increases (from the increase in speed), using , halving the volume leads to another doubling of pressure.

Step 3: Calculating the Total Increase in Pressure The total increase in pressure due to both effects: Thus, the percentage increase is:

Step 4: Verifying the Correct Option Comparing with the given options, the correct answer is:

Step 1: Understanding the Root Mean Square (rms) Speed Formula
The rms speed of gas molecules is given by: For two different gases at different temperatures:

Step 2: Substituting the Given Values
Given: and Using the formula:

Step 3: Solving for
Squaring both sides: Converting to Celsius:

Step 4: Conclusion
Thus, the required temperature is: