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The First Law of Thermodynamics is a fundamental principle in physics that explains how the energy of a system is conserved. Often referred to as the law of energy conservation, it states that energy cannot be created or destroyed in an isolated system. Instead, energy can be transformed from one form to another. For this exercise, remember how heat energy added to the system is converted into internal energy.The law is mathematically expressed as: \[\Delta Q = \Delta U + \Delta W\]where \( \Delta Q \) is the heat added to the system, \( \Delta U \) is the change in internal energy, and \( \Delta W \) is the work done by the system on its surroundings.In scenarios like heating water, if no physical work (e.g., expansion or compression) is done on the surroundings, \( \Delta W = 0 \). Hence, all the heat energy goes into changing the system's internal energy. This results in a simple relation: \( \Delta Q = \Delta U \). This means all the heat energy absorbed by the water contributes directly to increasing its internal energy.

Internal energy is the total energy contained within a system. It involves the movement and interactions of particles, which mean kinetic and potential energy at the molecular level. When you heat a substance like water, energy is added in the form of heat, increasing the water's internal energy.To calculate the change in internal energy (\( \Delta U \)) when heating water, you use the formula:\[\Delta U = c \cdot m \cdot \Delta T\]Here:

• \( c \) is the specific heat capacity, which measures how much energy is required to raise the temperature of a unit mass by one degree Kelvin.
• \( m \) is the mass of the substance, in this case, water.
• \( \Delta T \) is the change in temperature from the initial to the final state.

By applying this equation, the specific heat capacity of water, and knowing the mass and temperature change, you can determine the change in water's internal energy. This reflects the principle of how absorbing or releasing heat affects a substance's internal energy state.

Temperature conversion, especially between Celsius and Kelvin, is an essential step in thermodynamics calculations. The Kelvin scale is often used in scientific context because it is an absolute temperature scale.When dealing with temperature changes like \( \Delta T \), the same change applies whether you're using Celsius or Kelvin. This is because the size of one degree on both the Celsius and Kelvin scales are the same. For example, a temperature change from \( 21^{\circ} \text{C} \) to \( 37^{\circ} \text{C} \) results in \( \Delta T = 16 \) degrees, which is the same in Kelvin.It is crucial when performing calculations involving specific heat and energy change to convert temperatures into Kelvin when dealing with absolute values. Remember that Kelvin is \( 273.15 \) degrees greater than Celsius when converting presence of actual temperatures (e.g., \( T_{\text{K}} = T_{\text{C}} + 273.15 \)). However, for changes \( \Delta T \), the conversion isn't necessary since the change in magnitude is the same.