Final answer:
To find the energy transferred to a 2.0 kg aluminum cube with a temperature increase from 20°C to 60°C, use the specific heat capacity equation, resulting in 72 kJ of energy absorbed. For a 750 g water hot bottle cooling from 80°C to 20°C, the energy released is 188.37 kJ.
Step-by-step explanation:
To calculate the energy transferred to the aluminum cube when its temperature rises from 20°C to 60°C, we use the formula Q = mcΔT, where Q is the thermal energy transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature. In this case, m = 2.0 kg, c for aluminum is 900 J/(kg°C), and ΔT = (60°C - 20°C) = 40°C.
Therefore, Q = (2.0 kg)(900 J/kg°C)(40°C) = 72,000 J or 72 kJ.
For the second question, energy transferred out of the hot water bottle as it cools down can also be calculated using the same formula.
The mass m of the water is 750 g or 0.750 kg (since 1,000 g = 1 kg), the specific heat capacity c of water is 4,186 J/(kg°C), and the temperature change ΔT = (20°C - 80°C)
= -60°C (the negative sign indicates a decrease in temperature).
Thus, Q = (0.750 kg)(4,186 J/kg°C)(-60°C)
= -188,370 J, which means 188,370 J of energy was released. Since we are considering the amount of energy transferred out, we can remove the negative sign and say 188.37 kJ of energy was transferred out of the hot water bottle.