The Absorption of Heat by Solids and Liquids — Question 1

Question 1

A composite sample has additive heat capacity

A bonded assembly contains .400 kg of material A with $c_A=900\,\mathrm{J/(kg\,K)}$ and .600 kg of B with $c_B=400\,\mathrm{J/(kg\,K)}$. The parts remain at one temperature. Neglect bonding-layer capacity, losses and work; both specific heats are constant.

1. Find the assembly heat capacity and heat required for a 25.0 K rise.

2. Find its mass-averaged specific heat. How much material B must instead be used with the same .400 kg of A to make the assembly heat capacity 1000 J/K?

Question 1 - Solution

A composite sample has additive heat capacity

(a) Method and calculation

$$C=m_Ac_A+m_Bc_B=.400(900)+.600(400)=600\,\mathrm{J/K}.$$$$Q=C\Delta T=600(25)=15000\,\mathrm J.$$

(b) Interpretation and further calculation

$$c_{\mathrm{eff}}=\frac{C}{m_A+m_B}=600\,\mathrm{J/(kg\,K)}.$$$$360+400m_B=1000\ \Rightarrow\ m_B=1.60\,\mathrm{kg}.$$An unweighted average of the two specific heats would give 650 and is inappropriate for unequal masses.

Physical check

Heat capacity adds directly; specific heat must be weighted by mass.