Consider an aluminium calorimeter can with an aluminium stirrer has a total mass mAl and sepcific heat cAl. It contains a mass mw of water of specific heat
The correct answer and explanation is:
- An aluminum calorimeter can with an aluminum stirrer (combined mass = mAlm_{\text{Al}}, specific heat = cAlc_{\text{Al}})
- A mass of water, mwm_w, with specific heat cwc_w
- Possibly a temperature change due to adding a hot object or heat source
But the full question appears incomplete.
So let’s consider a typical calorimetry scenario, and provide the correct equation and a 300-word explanation:
Correct Answer (Equation):
When thermal equilibrium is reached after adding a hot object (e.g., a hot metal), the heat lost by the hot object equals the heat gained by the water and the aluminum container: Qlost=QgainedQ_{\text{lost}} = Q_{\text{gained}} mhotchot(Thot−Tf)=mwcw(Tf−Ti)+mAlcAl(Tf−Ti)m_{\text{hot}} c_{\text{hot}} (T_{\text{hot}} – T_f) = m_w c_w (T_f – T_i) + m_{\text{Al}} c_{\text{Al}} (T_f – T_i)
Where:
- mhot,chot,Thotm_{\text{hot}}, c_{\text{hot}}, T_{\text{hot}}: mass, specific heat, and initial temperature of the hot object
- TiT_i: initial temperature of water and aluminum can
- TfT_f: final equilibrium temperature
- mw,cwm_w, c_w: mass and specific heat of water
- mAl,cAlm_{\text{Al}}, c_{\text{Al}}: combined mass and specific heat of aluminum can and stirrer
300-Word Explanation:
In calorimetry, we use the principle of conservation of energy. When objects at different temperatures come into contact within an insulated system, no heat is lost to the environment. Instead, heat flows from the hotter object to the cooler ones until thermal equilibrium is reached.
In this case, the system includes a hot object (like a metal sample), water, and an aluminum calorimeter with a stirrer. Since the aluminum stirrer and can are both made of the same material and at the same temperature, we combine their masses into one term, mAlm_{\text{Al}}, and use the specific heat of aluminum, cAlc_{\text{Al}}, to calculate the heat gained.
The water and aluminum both absorb heat from the hot object. The heat gained by a substance is calculated using: Q=mcΔTQ = mc\Delta T
Where QQ is heat, mm is mass, cc is specific heat, and ΔT\Delta T is the change in temperature.
The final temperature TfT_f is common to all components in the system. The total heat gained by water and the aluminum container equals the heat lost by the hot object. By solving the heat balance equation, we can find the unknown, often TfT_f or the specific heat of the unknown object.
This method is a foundational technique in thermodynamics and experimental physics for measuring specific heat capacities and understanding energy transfer in physical systems.