Question 10: Can specific heat of a gas be zero or infinity? Can specific heat be negative?

Specific heat of a substance is defined as the amount of heat required to raise the temperature of a unit mass, (i-e, 1 kg) of a substance through unit temperature, i-e, 1K.
Mathematically,
C = ΔQ/mΔT
However, it should be remembered that specific heat is process dependent and not a unique or single value property of a substance. It may be positive, negative, zero or even infinity!
Consider the following case in which heat ΔQ is supplied to a gas of mass”m” contained in a cylinder provided with an airtight and frictionless piston. Then, C = ΔQ/mΔT ————- (1)
Now consider the following cases;
(1)The gas is suddenly compressed. Heat provided to the gas is zero but there is an increase in the temperature of the gas due to compression. Put ΔQ = 0 in equation (1),
C = 0/mΔT = 0
Therefore, specific heat C can be zero for this process (actually an adiabatic process).
(2) Let the gas be heated and allowed to expand at the same time. Suppose the fall of temperature due to expansion and raise in temperature due to the supply of heat are equal, then there would be no change in the temperature of the gas. Thus, ΔT = 0. Put in equation (1),
C = ΔQ/0 = ∞
Therefore, the specific heat can be infinity for this process (actually an isothermal process).
(3) Again let the fall in temperature due to expansion is less than the rise in the temperature due to heating, the temperature rises as the net effect. Putting a positive value (increase) of ΔT in equation (1), we get a positive value of the specific heat.
(4)Finally, let the fall in temperature due to expansion is greater than the rise in the temperature due to heating, then ΔT is negative. Putting a negative value in equation (1), we get a negative value for the specific heat.
Therefore, specific heat can be positive, negative, zero or infinity.