# Calculation of specific heat experimentally and mechanical equivalent of heat

After reading some books and some google searches and reading some answers on stack exchange physics what I have understand is (correct me if I am wrong) to calculate heat supplied we need change in temperature of the substance, amount of substance and specific heat of the substance (which depend on type f process also) from this equation Q=ms$$\Delta$$T.We can measure $$\Delta$$T and m so we just need specific heat to calculate heat.Specific heat can be determined experimentally and putting value in this equation $$m_1s_1\Delta T=m_2s_2\Delta T$$ we can determine the specific heat of the material.But it is written in the book that putting the value of specific heat of water as 4186/kg K we can determine the specific heat of the substance.But how do we know the specific heat of water, when I asked this doubt the answer what I found is that it is determined by Joule in his famous "Mechanical equivalent of heat ".Then I searched that and read some books in that it was given W=JH and then some methods are given to find J=4.186 J/cal. but in those methods values of specific heat is used to calculate J. so my doubt is how do we determine the specific heat of substance without knowing heat supplied.

The problem is that you have learned an old, antiquated definition of heat capacity that is incompatible with modern thermodynamics, and is incorrect when work is done on the system. The equation Q=mC\Delta T is correct only if work is not done. In modern thermodynamic, heat capacity is related to internal energy U, not heat. For a system at constant volume, $$\Delta U=mC_v\Delta T$$ and, from the first law of thermodynamics, we have $$\Delta U=mC_V\Delta T=Q-W$$. In a system where heat is exchanged, but no work is done $$\Delta U=MC_V\Delta T=Q$$but in a system where no heat is exchanged but work is done, the temperature rises and $$\Delta U=mC_v\Delta T=-W$$If a stirrer adds mechanical work to the system from the surroundings, W is negative, and we have $$C_v=\frac{-W}{m\Delta T}$$In Joule's experiment, he used a very accurate method of measuring the mechanical work -W that the stirrer did on the liquid water.
• So am I right in saying that to determine value of $C_v$ we need $\Delta T$,$\Delta Q$ and mass but heat can't be measured directly so we use $\Delta Q = \Delta W$ (in an isolated system) and by precise measurement of work we can determine the the value of $C_v$.And this is how we quantify heat and the number 4.184 comes from the earlier definition of one calorie Commented Sep 15, 2023 at 4:48
• But heat capacity defined as -"Heat capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature" so we need specific heat to quantify $\Delta Q$. If specific heat is defined in terms of internal energy how do we quantify heat. Commented Sep 16, 2023 at 5:34