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The concept of internal energy change is an important one in thermodynamics. It connects the energetic shifts within a system to temperature and amount of matter. Internal energy, represented often as \( \Delta U \), can be thought of as the sum of all molecular energies within a substance as they move and interact.

When a metal block, for example, is heated, its molecules gain more energy. This increased energy manifests as increased internal energy. To calculate this change, we use the equation:

• \( \Delta U = m \cdot c \cdot \Delta T \)

Here,

• \( m \) is the mass of the block,
• \( c \) is the specific heat capacity,
• \( \Delta T \) is the change in temperature.

By multiplying these three variables, we can see exactly how much energy was added or lost. Hence, if a solid metal block experiences heating, its internal energy increases because it absorbs heat to fuel the molecular motion.

Temperature change is a straightforward yet vital concept when dealing with heat and energy problems. It refers to how much warmer or cooler an object becomes. In formulas, this change is denoted by the Greek letter \( \Delta T \).

Calculating \( \Delta T \) is simple:

• You subtract the initial temperature \( T_1 \) from the final temperature \( T_2 \).

For instance, if a block's temperature goes from \( 15^{\circ} \text{C} \) to \( 90^{\circ} \text{C} \), the temperature change is:

• \( \Delta T = 90^{\circ} \text{C} - 15^{\circ} \text{C} = 75^{\circ} \text{C} \)

Temperature change is crucial in determining how much energy a material requires to heat or cool, according to its specific heat capacity. It helps us understand how much heat energy needs to be supplied or removed in heating systems or coolants.

Mass conversion is an essential step in many physics problems, particularly when units must align correctly for calculations. When solving heat transfer problems like changes in internal energy, converting mass from one unit to another ensures consistency.

In the given problem, the mass of the metal block is originally provided in kilograms (\( \text{kg} \)). Since the specific heat capacity is given in calories per gram \( (\text{cal/g} \cdot { }^{\circ}\text{C}) \), it's necessary to convert the mass to grams as well.

• The conversion factor is \( 1 \text{ kg} = 1000 \text{ g} \).
• Therefore, \( 2.0 \text{ kg} = 2000 \text{ g} \).

This conversion allows us to seamlessly integrate mass into the formula for calculating internal energy change, ensuring all measurements are compatible and the calculative result is accurate.