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The heat capacity of a substance can be defined as the amount of heat required to change its temperature by one degree.

Thermodynamicsin its totality is concerned about heat. The meaning of heat today is energy in transit. Before the development of thermodynamic laws, the heat was considered as the measure of an invisible fluid, caloric, present in any matter

Givenm

${\mathrm{m}}_{\mathrm{metal}}=0.5\mathrm{kg},,{\mathrm{m}}_{\mathrm{w}}=1\mathrm{kg}$

For water ${\mathrm{T}}_1=20掳\mathrm{C},,{\mathrm{T}}_2=22掳\mathrm{C},,,{\mathrm{T}}_1=100掳\mathrm{C}$

Solution

According to the given there is no change in phase so Q system: 0

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{w}}+{\mathrm{Q}}_{\mathrm{m}}+0 \\ {\mathrm{m}}_{\mathrm{w}}脳{\mathrm{C}}_{\mathrm{w}}脳{\mathrm{未罢}}_{\mathrm{w}}=-{\mathrm{m}}_{\mathrm{m}}脳{\mathrm{C}}_{\mathrm{m}}脳\mathrm{Tm} \end{gathered}$$

By solving for Cm

$$\begin{gathered} \mathrm{Cm}=-\frac{{\mathrm{M}}_{\mathrm{w}}{\mathrm{C}}_{\mathrm{w}}{\mathrm{未罢}}_{\mathrm{w}}}{{\mathrm{m}}_{\mathrm{m}}{\mathrm{未罢}}_{\mathrm{m}}} \\ =-\frac{1脳4190\mathrm{J}/\mathrm{kg}.\mathrm{K}\mathrm{x}{\left(22-20\right)}^0\mathrm{C}}{0.5\mathrm{kg}\mathrm{x}\left(22-100\right){\mathrm{C}}^0} \\ =215\mathrm{J}/\mathrm{kg}-\mathrm{K} \end{gathered}$$

Therefore the heat capacity of the metal is 215J/kgK

According to the result (a) We determine the specifc heat capacity of water higher than Cm of the metal, so water could absorb more heat and will store more Thermal energy-

Therefore the water of eqaul weight will store more thermal energy

If the heat absorbed by Styrofoam not negligible the quantity heat of metal must be larger, so Cm in result would be smaller

Therefore the Heat capacity of the metal will be smaller