Question

The root mean square velocity of an ideal gas in a closed container of the fixed volume is increased from $5\times {10}^4$ cm s${}^1$ to $10\times$ 10${}^4$ cm s${}^1$. Which of the following statement correctly explains how the change is accomplished:

• A. By heating the gas the temperature is doubled
• B. By heating the gas, the pressure is quandrupled (i.e., made four times)
• C. By heating the gas, the temperature is quadrupled
• D. By heating the gas the pressure is doubled

Answer 1

Answer: (B), (C)

The correct options are
B By heating the gas, the pressure is quandrupled (i.e., made four times)
C By heating the gas, the temperature is quadrupled

$V_{r.m.s}\propto \sqrt{T}$

So if velocity in increased two times than Temperature will increase by 4 times.

$PV=nRT$

Also, at fixed volume if pressure becomes four times by heating it will also increase the temperature to four times.