Three solid objects of the same material and of equal mass-a sphere, a cylinder (length = diameter) and a cube are at 500°C initially. These are dropped in a quenching bath containing a large volume of cooling oil each attaining the bath temperature eventually. The time required for 90% change in temperature is the smallest for

ANS:A - cube

The time required for 90% change in temperature will actually be the smallest for the cube. Explanation:

1. Surface Area to Volume Ratio: The rate of heat transfer is influenced by the surface area-to-volume ratio of the object. For a given volume, a cube has the largest surface area-to-volume ratio compared to a sphere and a cylinder.
2. Rate of Heat Transfer: Objects with larger surface area-to-volume ratios tend to lose or gain heat more quickly compared to those with smaller surface area-to-volume ratios. This is because a larger surface area provides more area for heat exchange with the surroundings.
3. Quenching Process: In the quenching process, the objects are immersed in a cooling bath containing oil, and heat is transferred from the objects to the surrounding oil. The rate of heat transfer from the objects to the oil determines how quickly the objects cool down.
4. Cube's Advantage: Due to its larger surface area-to-volume ratio, the cube has more surface area through which heat can be transferred to the surrounding oil. As a result, it will cool down more quickly compared to the sphere and the cylinder.
5. Time Required for Cooling: Since the cube cools down more quickly than the other shapes due to its larger surface area-to-volume ratio, it will take the shortest time to reach the bath temperature. Therefore, the time required for 90% change in temperature will be the smallest for the cube.