91Ó°ÊÓ

When trying to understand the concept of specific heat capacity, think about how much energy it takes to change the temperature of a substance. For water, this number is quite large. The specific heat capacity of water is 4,186 Joules per kilogram per degree Celsius (J/kg°C).
This means you need 4,186 Joules of energy to heat 1 kilogram of water by just 1°C.
Specific heat capacity is an important concept in many heating applications, as it determines how much energy you need to heat up a substance. If you have a high specific heat capacity, like water, you need to input a lot of energy to see a temperature change.
Considering the example, if you start with water at 19°C and want to heat it to 100°C, you'll need to input a significant amount of energy to make this happen. Specifically, the energy needed can be calculated with the formula: \[ Q = m \times c \times \Delta T \]where:

• \( Q \) is the energy in Joules,
• \( m \) is the mass in kilograms,
• \( c \) is the specific heat capacity,
• \( \Delta T \) is the temperature change.

Potential energy is a form of stored energy that depends on the position of an object. In our exercise, potential energy is at play every time you shake the water in the thermos flask. As the water falls, it converts potential energy into thermal energy.
To calculate the potential energy gained or lost by an object due to a change in its height, you can use the formula: \[ PE = m \times g \times h \]where:

• \( PE \) is the potential energy in Joules,
• \( m \) is the mass in kilograms,
• \( g \) is the acceleration due to gravity (approximately 9.81 m/s² on Earth),
• \( h \) is the height in meters.

In this exercise, each shake of the flask results in the water falling a height of 0.32 meters.
This action converts the potential energy of the water into thermal energy, which contributes to raising its temperature. With each shake, small amounts of energy are transferred to the water, slowly increasing its overall energy and consequently its temperature.

Whenever you increase or decrease the temperature of a substance, you're affecting its internal energy. The concept of temperature change refers to the difference between the final and initial temperatures. Here, the challenge is to raise the water's temperature from 19°C to 100°C.
Using the formula for energy required based on specific heat capacity, we can determine how much energy is necessary for this temperature change. The formula: \[ Q = m \times c \times \Delta T \]helps us understand that you need the initial and final temperatures to calculate the \( \Delta T \) (change in temperature).
In our example, the change in temperature, \( \Delta T \), is:

• 100°C (final temperature) - 19°C (initial temperature) = 81°C

This 81°C change embodies the amount of heating or energy transfer needed to boil the water.
It is only through understanding this change that we can effectively plan out our energy input and how long the process might take, especially in constrained heating scenarios like using shakes in a thermos.