Heat Transfer

When a monoatomic ideal gas expands at constant pressure, part of the supplied heat energy is used to do work and the rest increases the internal energy of the gas. For an ideal gas expanding at constant pressure, the heat energy supplied is given by the formula: Where:
is the total heat energy supplied,
is the change in internal energy,
is the work done by the gas.
For a monoatomic ideal gas, the change in internal energy is given by:
The work done by the gas during expansion at constant pressure is: The fraction of heat energy converted into work is: Thus, the fraction of heat energy converted into work is .

The rate at which an object cools is determined by the surface area and volume.
According to Newton's law of cooling, the rate of heat loss is directly proportional to the surface area and inversely proportional to the volume.
The sphere has the least surface area for a given volume, which makes it lose heat more slowly.
The plate has the greatest surface area relative to its volume, allowing it to cool down the fastest.
The cube has a moderate surface area and will cool at a rate between the sphere and plate.

Thus, the plate will cool the fastest and the sphere the slowest.