Two ideal gases $A$ and $B$ of the same number of moles expand at constant temperatures $T_1$ and $T_2$ respectively such that the pressure of gas $A$ decreases by $50 \%$ and the pressure of gas $B$ decreases by $75 \%$. If the work done by both the gases is same, then $T_1: T_2$ is:

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is ${m_A}$ and that in $B$ is ${m_B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then:

$A$ perfect gas of volume $5 \ L$ is compressed isothermally to a volume of $1 \ L$. The $r.m.s.$ speed of the molecules will

An ideal gas at pressure $P$ is enclosed in a container that is placed in a reservoir at temperature $T$. If the volume of the gas is increased to two times its original value,then the new pressure $P^{\prime}$ is equal to:

When heat is given to a gas in an isothermal process,then there will be

For an isothermal expansion of a perfect gas,the value of $\frac{\Delta P}{P}$ is equal to: