(ii) fundamental interval.
(b) List two uses of the hydraulic press.
(c) Name the material used to reset the steel index in the Six's maximum and minimum thermometer.
(d)(i) A nursing mother prepared her baby's milk mixture at 85°C, in a feeding bottle. In order to cool it to 40°C, she immersed the bottle in an aluminium bowl of heat capacity 90 JK\(^{-1}\) containing 500 g of water at 26°C. If the mass of the mixture is 300g, calculate the specific heat capacity of the mixture. [Neglect heat losses and heat capacity of the bottle; specific heat capacity of water = 4200 J kg\(^{-1}\) K\(^{-1}\)]
(ii) (\(\alpha\)) Name two ways through which the bottle losses heat.
(\(\beta\)) Name two industrial processes in which heat exchanger is used.
(a)(i) Thermal equilibrium: the state reached when two (or more) bodies in thermal contact are at the same temperature so that there is no net flow of heat between them.
(a)(ii) Fundamental interval: the temperature range between the lower fixed point (ice point) and the upper fixed point (steam point) of a thermometer scale.
(b) Two uses of the hydraulic press:
- Lifting heavy loads (e.g. hydraulic jack / car lift).
- Compressing or baling materials such as cotton, scrap metal and refuse (also forging and stamping metals).
(c) Material used to reset the steel index in the Six's maximum and minimum thermometer: a magnet (the steel indices are drawn back with a small magnet).
(d)(i) Specific heat capacity of the mixture.
Heat lost by the hot milk mixture = heat gained by the water + heat gained by the aluminium bowl.
Mixture: \(m=300\,\text{g}=0.3\,\text{kg}\), cools \(85^{\circ}\text{C}\to40^{\circ}\text{C}\), \(\Delta\theta=45\,\text{K}\).
Water: \(0.5\,\text{kg}\), warms \(26^{\circ}\text{C}\to40^{\circ}\text{C}\), \(\Delta\theta=14\,\text{K}\).
Bowl heat capacity \(=90\,\text{JK}^{-1}\), warms by \(14\,\text{K}\).
\[ 0.3\,c\,(45) = (0.5)(4200)(14) + (90)(14) \]\[ 13.5\,c = 29400 + 1260 = 30660 \]\[ c = \frac{30660}{13.5} = 2271\,\text{Jkg}^{-1}\text{K}^{-1} \]
So \(c \approx 2.27\times10^{3}\,\text{Jkg}^{-1}\text{K}^{-1}\).
(d)(ii)(\(\alpha\)) Two ways the bottle loses heat: conduction and convection (radiation and evaporation are also acceptable).
(d)(ii)(\(\beta\)) Two industrial processes using a heat exchanger: electricity generation in power stations (steam condensers/boilers) and refrigeration / air-conditioning (also petroleum refining and food pasteurization).
