Heat is removed from a molten metal of mass $$2$$ $$kg$$ at a constant rate of $$10$$ $$kW$$ till it is completely solidified. The cooling curve is shown in the figure.

Assuming uniform temperature throughout the volume of the metal during solidification, the latent heat of fusion of the metal (in $$kJ/kg$$) is ______________

A cylindrical job with diameter of $$200$$ $$mm$$ and height of $$100$$ $$mm$$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $$mm$$) is

A $$300$$ $$mm$$ thick slab is being cold rolled ussing roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______

A $$300$$ $$mm$$ thick slab is being cold rolled using roll of $$600$$ $$mm$$ diameter. If the coefficient of friction is $$0.08,$$ the maximum possible reduction (in $$mm$$) is _______________