If in general the specific heat capacity is low in gas then why doesn't it raise it's temperature more quickly compared to a solid that is given similar conditions as to the gas. (By the reason of the definition of s.h.c. is "heat that should be transferred in order to change an unit temperature in 1 kg" )if so then by giving similar heat energy to both solid and gas , gas should have the high temperature .why not? Please explain
[Physics] Specific heat capacity in gas vs solid
gassolid-state-physicsthermal conductivity
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Can any solid material with a low heat capacity exist that feels closer to human body temperature than another solid material with a higher heat capacity; where both materials were previously kept in either a mundane oven or freezer for a sustained period?
Let me rephrase to:
Is there any solid which disobeys the inverse proportionality of thermal conductivity and specific heat capacity?
Consider $1000kg$ of wood and $1000kg$ of aluminium, both at $320K$ (very warm). At the instant you place a finger on such large thermal masses, your perception of temperature comparison is dependent on heat conductivity of the materials, not their heat capacity (their masses are so large compared to your finger, their temperature is almost constant depsite losing heat to your finger). Using such large masses and (equal masses for that matter) is necessary since otherwise I can instantly answer yes to your question by giving you 100g of wood and 1g of gold (beaten to the same surface area of the wood) just taken from the freezer and you would perceive gold being closer to body temperature than the wood after a second. So lets define the question by specific heat capacity, and instantaneous perception of heat transfer.
To answer it though, there is in fact no metal which disobeys this relation due to the electron sea being the majority carrier of kinetic energy in the bulk metal. Their having large mean free paths and low masses allow them to attain very high velocities (which is a property of high temperature) and therefore are able to transfer energy quickly in the bulk material. In other words, if metals used anything heavier to transmit heat, like their nuclei, it would not only take much more heat to accelerate them to the same velocities the electrons could attain (resulting in higher heat capacity), but the rate at which that kinetic energy is transmitted across the material is accordingly slower (lower thermal conductivity). In fact the lattice of metal nuclei do in fact contribute to both properties via phonons not translational kinetic energy like in gases, but phonons are still greatly superseded by the effect from electrons. Therefore the inverse relation between thermal conductivity and heat capacity is valid for metals.
What you are looking for is a non conductor with both higher heat capacity and thermal conductivity than a conductor. For that I give you diamond (figuratively...I can't afford one), which has a specific heat capacity of $0.5 J/gK$, higher than that of any metal denser than vanadium (which is almost all of them), but has a thermal conductivity of $>900W/mK$, trumping silver's $421W/mK$ which is tops for all pure metals.
Indeed, $1kg$ of silver would feel much closer to body temperature than $1kg$ of diamond (that's alot of diamond!) despite diamond having a higher heat capacity.
The thermal energy for each degree of freedom is given by $$\frac{1}{2} k_{B} T $$ If this thermal energy is lower than the gap between ground state and first excited state (supposing quantised energy levels) then a thermal excitation becomes very unlikely. I would guess that this is what the author means by "frozen" degrees of freedom.
For a more precise answer it would help if you would give the reference of your quote.
Best Answer
"Specific heat capacity" is defined as the amount of heat absorbed or released by an unit mass of a substance when it's temperature changes by one unit. Yeah you are right, specific heat capacity for gases is low because less amount of heat supplied can change it's temperature by one unit whereas solids require more heating for it's temperature to change by one unit.
$$S = \frac{\delta Q}{m\,\delta T}$$
Here is some data regarding specific heat capacities of water in it's different states,
$$\mathrm {Steam} : 2010\,J/ kg\,°C$$ $$\mathrm {Ice} : 2090\,J/ kg\,°C$$ $$\mathrm {Water(liquid)} : 4200\,J/ kg\,°C$$
You could see that heat capacity for steam is lower than the ice, but the difference is not that significant in this case,
The trends in specific heat capacity has lots of exceptions but depends on the properties(such as hydrogen bonding and dipole interactions) of the subsatance.
But in general, the order of specific heat capacity for different states is $$Gas<Solid<Liquid$$
When we consider ideal states of matter, liquids generaly absorb or release more heat(for a unit change in temperature) because they exchange energy through both translational and vibrational modes whereas gases and solids do so only by translational and vibrational respectively.