Find the change in the internal energy of 2 kg of water as it is heated from 0^∘ C to 4^∘ C. Th

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Find the change in the internal energy of 2 kg of water as...

Find the change in the internal energy of $2 \mathrm{~kg}$ of water as it is heated from $0^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$. The specific heat capacity of water is $4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ and its densities at $0^{\circ} \mathrm{C}$ and $4^{\circ} \mathrm{C}$ are $999 \cdot 9 \mathrm{~kg} \mathrm{~m}^{-3}$ and $1000 \mathrm{~kg} \mathrm{~m}^{-3}$ respectively. Atmospheric pressure $=10^{5} \mathrm{~Pa}$.

Key Concepts

Density and Volume Relationship

Density, defined as mass per unit volume, is an important property for establishing the volume occupied by a substance given its mass. In thermodynamics, variations in density due to temperature changes can lead to changes in volume, which in turn affect the work done by or on the system. This relationship is particularly useful for problems where physical properties like volume and pressure are interdependent.

Internal Energy

Internal energy is the total energy contained within a system due to both the microscopic motions and interactions of its particles. It is a state function, meaning its value depends only on the current state of the system, regardless of the path taken to reach that state. In thermodynamics, changes in internal energy are analyzed to understand how a system responds to heat transfer and work interactions.

First Law of Thermodynamics

The First Law of Thermodynamics is a statement of energy conservation for thermodynamic systems. It asserts that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system on its surroundings. This principle provides the fundamental framework for analyzing energy transfer processes including heating and expansion or compression.

Specific Heat Capacity

Specific heat capacity is a physical property that quantifies the amount of heat required to raise the temperature of a unit mass of a substance by one degree Kelvin. It is crucial for calculating the amount of energy added to or removed from a system as its temperature changes, and it helps in determining the thermal response of the material.

Work in Thermodynamic Processes

Work in thermodynamic processes refers to the energy transfer associated with volume changes of a system under pressure. When a system expands or compresses, it does work on its surroundings or has work done on it. The work done in a constant pressure process, for example, is computed as the product of the pressure and the change in volume, and it is essential when assessing the total energy change in the system.

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