# Thermal Capacity

An electrical heating coil of power $P$ is used to transfer thermal energy to a body of mass $m$. In a time $t$ the body changes temperature by $\Delta T$ . What is the thermal capacity of the body?

The question has asked for Heat capacity(which is independent of mass) and NOT specific heat capacity(which depends on mass) thus the answer is $\ C = \frac {Pt}{ \Delta T}$

Remember two things:

1. Heat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change.(Denoted by the capital letter 'C')
2. The specific heat capacity is the heat capacity per unit mass of a material.(Denoted by the small letter 'c')

Work done by the coil can be calculated by $$\ W = Pt$$ This amount of work is contributed to heat the body (in this case the efficiency is 100%). $$\ W = Q_{heat}$$ Also, ($\ c$ is the thermal capacity) $$\ Q = cm\Delta T$$ Therefore, combine the equations above, we get: $$\ c = \frac {Pt}{m \Delta T}$$

• Thanks for anwering however the right result is Pt/ΔT but I really dont understand why – Claudio Giannini Apr 30 '16 at 15:26
• There's no work involved here. $Q_{heat}=Pt$, $Q_{heat}=mc\Delta T$. So, indeed, $c=\frac{Pt}{m\Delta T}$. – Gert Apr 30 '16 at 16:39
• @ClaudioGiannini: this problem does involve mass $m$. Intuitively: a larger mass will require more heat to get to the same temperature than a smaller one. en.wikipedia.org/wiki/Heat_capacity – Gert Apr 30 '16 at 16:42
• It may be that $c$ is the specific thermal capacity, i.e. the thermal capacity per unit mass and what is wanted is $mc$. – jim Apr 30 '16 at 16:46