An ideal monatomic gas of $n$ moles is taken through a cycle $W X Y Z W$ consisting of consecutive adiabatic and isobaric quasi-static processes, as shown in the schematic $V-T$ diagram. The volume of the gas at $W, X$ and $Y$ points are, $64 \mathrm{~cm}^3, 125 \mathrm{~cm}^3$ and $250 \mathrm{~cm}^3$, respectively. If the absolute temperature of the gas $T_W$ at the point $W$ is such that $n R T_W=1 \mathrm{~J}$ ( $R$ is the universal gas constant), then the amount of heat absorbed (in J ) by the gas along the path $X Y$ is ___________.

A geostationary satellite above the equator is orbiting around the earth at a fixed distance $r_1$ from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance $r_2$ from the center of the earth, such that $r_1=1.21 r_2$. The time period of the second satellite as measured from the geostationary satellite is $\frac{24}{p}$ hours. The value of $p$ is _________.

The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2 L}{5}$. In thermodynamic equilibrium, the piston is a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P=\frac{k L}{A} \alpha$, then the value of $\alpha$ is __________.

In a Young's double slit experiment, a combination of two glass wedges $A$ and $B$, having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is $d=2 \mathrm{~mm}$ and the shortest distance between the slits and the screen is $D=2 \mathrm{~m}$. Thickness of the combination of the wedges is $t=12 \mu \mathrm{~m}$. The value of $l$ as shown in the figure is 1 mm . Neglect any refraction effect at the slanted interface of the wedges. Due to the combination of the wedges, the central maximum shifts (in mm ) with respect to O by ____________.