specific heat capacity

1. There is no simple relationship between the two (heat conductivity and specific heat capacity), as each of which is attributed to different physical mechanisms.

Thermal conductivity of a subatance depends on the amount of free electrons, because heat conduction is carried out by vibrations of these free eelctrons. This is the reason why metals (which have abundance of free electrons) are generally good thermal conductors than non-metals. For the same reason, it is apparent that good thermal conductors are also good eelctrical conductors due to the presence of free electrons.

On the other hand, specific heat capacity is attributed by lattice vibration (molecular vibration) of substances. It thus depends on the bonding (i.e. intermolecular force) between molecules.

2. Definite NOT. Simply becuase they are of different sates, and hence under different degrees of intermolecular force.

The specific heat capacity of water is about 4.18 kJ/kg-K. The specific heat capacity of steam is about 2 kJ/kg-K, which is less than half of that for water.

The reason for that is simply steam molecules are under very weak intermolecular force, thus they can move freely. Heating of the steam would provide energy that will ALL go to the kinetic energy of these molecules, and give rise to an increase of temperature.

Because of intermolecular force is not negligible in water in the liquid state, the energy in heating water will go partly to the kinetic energy of water molecules and the rest to the potential energy of the molecules. The former gives to a rise of temperature, whereas the latter gives the expansion of liquid water. It is therefore very clear that steam requires less energy for a degree rise in temperature than liquid water, thus steam has lower specific heat capacity than liquid water does.

3. Definitely NO. Specific heat capacity of any substance is temperature dependent.

For liquid water, the specific heat capacity is at 4.21 kJ/kg-K at 0' C, then decreases as temperature rises until a minimum of 4.178 kJ/kg-K at 35'C. The specific heat capacity then rises again with temperature, to a value of 4.219 kJ/kg-K at 100'C.

Please refer to the following web-page for detailed variation of the specific heat capacity of water with temperature.

http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html