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Specific heat capacity is a property that tells us how much heat energy needs to be added to a substance to change its temperature by one degree Celsius per unit mass.
It's measured in joules per kilogram per degree Celsius \(J/(kg \cdot °C) \). When you know the specific heat capacity of a material, you can predict how much its temperature will change when a certain amount of heat is added.
Here, for this material block, the specific heat capacity is given as 750 J/(kg°C).
In simpler terms, a higher specific heat capacity means the material can absorb more heat without a large change in temperature. This concept is crucial in calculating the amount of heat required to change the volume of a block because every bit of heat we provide changes the temperature, which in turn affects the volume due to thermal expansion.
Understanding this concept helps relate heat input to temperature changes in any thermal dynamics problem.

The coefficient of volume expansion is a measure of how much the volume of a material changes with temperature.
It is expressed as \(\beta\), and for our material, \(\beta = 6.4 \times 10^{-5} \ \text{°C}^{-1}\).
This means for every increase of one degree Celsius in the material's temperature, its volume will increase by a factor of \(6.4 \times 10^{-5}\) times its original volume.
This property is key when dealing with volume changes due to heat. Furthermore, it directly relates to how much temperature change is needed to achieve a certain change in volume.
Using the combined knowledge of specific heat capacity and the coefficient of volume expansion allows us to determine how much heat leads to a specific volume increase. The formula \(\Delta V = \beta V_0 \Delta T\) connects these concepts by relating the temperature change that causes a change in volume.

Heat transfer is the movement of heat energy from one place or material to another.
In our scenario, heat transfer is responsible for increasing the temperature of the block, which consequently causes it to expand.
The heat energy required to cause this volume expansion can be calculated using the formula \(Q = mc\Delta T\). Here, \(Q\) is the total heat energy, \(m\) is the mass, \(c\) is the specific heat capacity, and \(\Delta T\) is the temperature change.
These calculations rely on understanding that heat transfer into the block results in an increase in the internal energy, manifested through temperature rise and expansion.
For practical purposes:

• Determine the energy needed to raise the temperature first.
• Apply this to the formula to calculate the heat needed.
• This approach keeps calculations organized and easy to understand.

With these principles, students can better grasp how heat energy impacts physical changes in volume and temperature.