Calculate the internal energy change for each of the...

Calculate the internal energy change for each of the following. a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases $23 \mathrm{~J}$ of heat. b. A piston is compressed from a volume of $8.30 \mathrm{~L}$ to $2.80 \mathrm{~L}$ against a constant pressure of $1.90 \mathrm{~atm} .$ In the process, there is a heat gain by the system of $350 . \mathrm{J}$. c. A piston expands against $1.00 \mathrm{~atm}$ of pressure from $11.2 \mathrm{~L}$ to $29.1 \mathrm{~L}$. In the process, $1037 \mathrm{~J}$ of heat is absorbed.

Calculate the internal energy change for each of the following.
a. One hundred (100.) joules of work is required to compress a gas. At the same time, the gas releases $23 \mathrm{~J}$ of heat.
b. A piston is compressed from a volume of $8.30 \mathrm{~L}$ to $2.80 \mathrm{~L}$ against a constant pressure of $1.90 \mathrm{~atm} .$ In the process, there is a heat gain by the system of $350 . \mathrm{J}$.
c. A piston expands against $1.00 \mathrm{~atm}$ of pressure from $11.2 \mathrm{~L}$ to $29.1 \mathrm{~L}$. In the process, $1037 \mathrm{~J}$ of heat is absorbed.

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics is the principle of energy conservation applied to thermodynamic processes. It states that the change in the internal energy of a system, ?U, is equal to the sum of the heat transferred into the system, Q, and the work done on the system, W. This relation, expressed as ?U = Q + W, is fundamental for calculating energy changes during processes such as compression or expansion.

Heat Transfer

Heat transfer refers to the energy exchanged due to a temperature difference between the system and its surroundings. In thermodynamic calculations, the sign of the heat is important: positive Q indicates heat absorbed (gained) by the system, while negative Q indicates heat released (lost) by the system. The concept is crucial for determining the direction of energy flow in a process.

Work Done on a System

Work done on or by the system is another key component in thermodynamic processes. The sign of work in the energy balance depends on the convention used; here, work done on the system is taken as positive, meaning that when the system is compressed (work is done on it), W is positive, and when the system expands (it does work on the surroundings), W is negative. Understanding this sign convention is pivotal for correctly applying the first law of thermodynamics.

Unit Conversions in Thermodynamics

In thermodynamics, it is often necessary to convert between different units of energy. For example, work calculated from pressure and volume changes may be expressed in liter-atmospheres (L?atm), which can be converted to joules using the relation 1 L?atm ? 101.3 J. This conversion ensures consistency of units when applying the first law of thermodynamics to compute internal energy changes.

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