Lesson Notes By Weeks and Term v4 - SHS 2
HEAT
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HEAT
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Subject: Physics
Class: SHS 2
Term: 1st Term
Week: 13
Grade code: 2.2.1.LI.2
Strand code: 2
Sub-strand code: 1
Content standard code: 2.2.1.CS.1
Indicator code: 2.2.1.LI.2
Theme: ENERGY
Subtheme: HEAT
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This lesson introduces the concepts of heat capacity and specific heat capacity. We will explore why some substances, like water in a cooking pot, take a long time to heat up, while others, like the metal of the pot itself, heat up very quickly. Understanding this principle is crucial for many everyday applications in our homes and industries in Ghana, from cooking our favourite meals like *banku* and *fufu* to understanding local weather patterns like the sea breeze along our coast. This lesson encourages collaborative learning, valuing the unique perspectives and skills that each student, regardless of their background, brings to our scientific discussions.
A. Recap: Heat vs. Temperature Before we begin, let's remember the difference: Heat (Q) is the thermal energy transferred from a hotter object to a colder object. Its SI unit is the Joule (J). Temperature (θ) is a measure of the degree of hotness or coldness of a body. It indicates the average kinetic energy of the particles in a substance. Its SI unit is the Kelvin (K), but we often use degrees Celsius (°C). A change of 1 K is equal to a change of 1°C. B. Heat Capacity (C) Imagine you have a small stone and a large rock sitting in the sun. To raise the temperature of both by just 1°C, you would need to supply much more heat energy to the large rock. This property is called heat capacity. Definition: Heat capacity is the quantity of heat energy required to raise the temperature of an entire body or object by one degree Kelvin (1 K) or one degree Celsius (1°C). Formula: `C = Q / Δθ` Where: `C` = Heat Capacity `Q` = Heat energy supplied (in Joules, J) `Δθ` = Change in temperature (in K or °C), calculated as (Final Temperature - Initial Temperature) Unit: Joules per Kelvin (J/K) or Joules per degree Celsius (J/°C). Key Idea: Heat capacity depends on both the *material* and the *mass* of the object. A larger object has a higher heat capacity. C. Specific Heat Capacity (c) Now, what if we want to compare materials themselves, without worrying about the size or mass of the object? We need a *specific* value. This is where specific heat capacity comes in. Definition: Specific heat capacity is the quantity of heat energy required to raise the temperature of a unit mass (1 kg) of a substance by one degree Kelvin (1 K) or one degree Celsius (1°C). Formula: `c = Q / (m * Δθ)` This is more commonly rearranged and used as: `Q = mcΔθ` Where: `Q` = Heat energy supplied (J) `m` = mass of the substance (kg) `c` = specific heat capacity of the substance (J/kgK or J/kg°C) `Δθ` = change in temperature (K or °C) Unit: Joules per kilogram per Kelvin (J/kgK) or Joules per kilogram per degree Celsius (J/kg°C). Key Idea: Specific heat capacity is an intrinsic property of a *substance*. It does not depend on the mass. For example, water has a very high specific heat capacity (approx. 4200 J/kgK), while copper has a much lower one (approx. 390 J/kgK). This means it takes much more energy to heat 1 kg of water by 1°C than to heat 1 kg of copper by 1°C. D. Relationship Between Heat Capacity (C) and Specific Heat Capacity (c) From the definitions, we can see a clear link: Heat Capacity `C = Q / Δθ` Specific Heat Capacity `c = Q / (mΔθ)` If we rearrange the second formula, we get `Q/Δθ = mc`. Since `C = Q/Δθ`, we can substitute to get: `C = mc` > In simple terms: The heat capacity of an object is its specific heat capacity multiplied by its mass.
E. Determining Specific Heat Capacity Experimentally Method of Mixtures This is the most common laboratory method. It relies on the principle of conservation of energy. Principle: When a hot object is mixed with a cold object in an insulated container (a calorimeter), and no heat is lost to the surroundings: Heat Lost by Hot Object = Heat Gained by Cold Object(s) Procedure (to find 'c' of a solid, e.g., a metal block): Measure the mass of the metal block (`m_b`). Heat the block in boiling water (or a steam chest) for some time. Its temperature will be that of the boiling water, `θ_h` (approx. 100°C). Measure the mass of an empty calorimeter (`m_cal`) and its stirrer. Then add some cold water and measure the mass again. The mass of the water is `m_w` = (mass of calorimeter + water) - `m_cal`. Record the initial temperature of the cold water and calorimeter, `θ_c`. Quickly transfer the hot metal block from the boiling water into the calorimeter. Stir the water gently and record the highest steady temperature reached. This is the final temperature of the mixture, `θ_f`. Calculation: Heat lost by hot block: `Q_lost = m_b * c_b * (θ_h - θ_f)` Heat gained by cold water: `Q_gained_water = m_w * c_w * (θ_f - θ_c)` Heat gained by calorimeter: `Q_gained_cal = m_cal * c_cal * (θ_f - θ_c)`
Applying the principle: `Q_lost = Q_gained_water + Q_gained_cal` `m_b * c_b * (θ_h - θ_f) = m_w * c_w * (θ_f - θ_c) + m_cal * c_cal * (θ_f - θ_c)` This can be simplified to: `m_b * c_b * (θ_h - θ_f) = (m_w * c_w + m_cal * c_cal) * (θ_f - θ_c)`
You can then rearrange this formula to solve for the specific heat capacity of the block, `c_b`. *(Note: The specific heat capacities of water (`c_w`) and the calorimeter material (`c_cal`, usually copper or aluminium) must be known).*