A gas is compressed adiabatically till its temperature is doubled. The ratio of its final volume to initial volume will be

Figure shows, the adiabatic curve on a $\log T$ and log $V$ scale performed on ideal gas. The gas is ............

In the following $P-V$ diagram two adiabatics cut two isothermals at temperatures $T_1$ and $T_2$ (fig.). The value of $\frac{{{V_a}}}{{{V_d}}}$ will be

A cylinder with a movable piston contains $3\,moles$ of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increases if the gas is compressed to half its original volume? 

Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)

During the adiabatic expansion of $2 \,moles$ of a gas, the internal energy was found to have decreased by $100 J$. The work done by the gas in this process is ..... $J$