# Specific heat capacity of a body and mechanical equivalent?

My textbook states that

"If the temperature of a substance changes without the transfer if heat ($Q=0$), then $S=Q/(m$∆$T)=0$ Thus, when liquid in a thermos flask is shaken, its temperature increases without the transfer of heat and hence, the specific heat of liquid in the thermos flask is zero."

My doubt is this: we are well aware about the mechanical equivalent of heat; we know that doing a certain amount of work, $W$ on a body is equivalent to supplying the same body with an equivalent amount of heat, $Q$, given by

$$Q=W/J$$

Where $J$ is the mechanical equivalent of heat, which is a universal constant. In the situation described by my textbook, the temperature of the system is increasing due to the work that we are doing on it by shaking the thermos flask. Using the above expression, we are able to calculate the equivalent amount of heat for this work done. If we were to substitute this value of $Q$ in the formula $mS\mathrm{d}T=\mathrm{d}Q$ we'd definitely obtain a nonzero value for $S$.

What is the basic fault in my reasoning?

Edit: Please don't ask me to propose a method using which we can measure the exact amount of work done on the body (by shaking, in this case) for I don't know how. Please let me know if this inability to measure that exact amount of work done is the basic problem.

• In my judgment, your reasoning is flawless, and you should get rid of your textbook. Saying that the specific heat of the liquid in the flask is zero is totally incorrect, since specific heat is a physical property of the liquid, that is unrelated to any process that the liquid is subjected to. – Chet Miller Sep 18 '16 at 13:20
• I second @ChesterMiller's suggestion that you should get rid of that textbook. I suggest you begin with Thermodynamics by Fermi, which is simply and very well written. – Deep Sep 19 '16 at 7:00
• The specific heat capacity of a material is indeed a state function. However, heat capacity is indeed different for different processes. By your argument, one will be lead to believe that the heat capacity of a material undergoing an adiabatic process is some non-zero number, no? Apparently, this is false and any system undergoing an adiabatic process has heat capacity value of zero.(You may Google this to verify). This is how heat capacity is defined. Nevertheless, there is still some doubt regarding this particular case of shaking the bottle. If you could elaborate on that please..? – user106570 Sep 20 '16 at 7:51
• Which textbook? – valerio Nov 15 '16 at 8:32

There's no fault. Your reasoning is correct. If you input an equivalent heat in the formula, you get the equivalent specific heat $S$ as a result.
Bear in mind that the formula $Q=Sm\Delta T$ tells the temperature change that addition (or removal) of heat would cause. If there's no heat, $Q=0$, there's no temperature change caused by heating, $\Delta T$. The specific heat capacity $S$ is a material constant and is not "suddenly" zero - there seems to be a flaw in the quote you've presented.