The condition $dw = dq$ holds good in the following process:

The thermodynamic process,in which the internal energy of the system remains constant is ...........

For an ideal gas, in an isothermal process:

The work done by an ideal gas of $2 \text{ moles}$ in increasing its volume from $V$ to $2V$ at constant temperature $T$ is $W$. The work done by an ideal gas of $4 \text{ moles}$ in increasing its volume from $V$ to $8V$ at constant temperature $\frac{T}{2}$ is:

The specific heat of a gas in an isothermal process is

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: