$100 \, mL$ of $O_2$ and $H_2$ are kept at the same temperature and pressure. Which of the following is true regarding the number of molecules?

What is the new temperature of a gas when its initial volume $3 \ dm^3$ at $300 \ K$ is doubled at constant pressure (in $K$)?

The density of an ideal gas can be given by where $P$,$V$,$M$,$T$ and $R$ respectively denote pressure,volume,molar mass,temperature and universal gas constant.

$A$ vessel contains $1.6 \ g$ of dioxygen at $STP$ ($273.15 \ K$,$1 \ atm$ pressure). The gas is now transferred to another vessel at constant temperature,where pressure becomes half of the original pressure. Calculate
$(A)$ volume of the new vessel.
$(B)$ number of molecules of dioxygen.

The following graph shows a system containing $1 \ mole$ of gas undergoing various steps. When it moves from $z$ to $x$, the type of process is:

When an ideal gas undergoes free expansion,then: