(II) Consider the following two-step process. Heat is...

(II) Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a volume of 5.9 $\mathrm{L}$ to $9.3 \mathrm{L},$ where the temperature reaches its original value. See Fig. $30 .$ Calculate $(a)$ the total work done by the gas in the process, (b) the change in internal energy of the gas in the process, and (c) the total heat flow into or out of the gas.

(II) Consider the following two-step process. Heat is
allowed to flow out of an ideal gas at constant volume so
that its pressure drops from 2.2 atm to 1.4 atm. Then the gas
expands at constant pressure, from a volume of 5.9 $\mathrm{L}$ to
$9.3 \mathrm{L},$ where the temperature reaches its original value.
See Fig. $30 .$ Calculate $(a)$ the total work done by the
gas in the process,
(b) the change in
internal energy of
the gas in the
process, and (c) the
total heat flow into
or out of the gas.

Key Concepts

Ideal Gas Law

This law, expressed as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas with the amount of gas (n) and the gas constant (R). It is crucial for understanding how state variables change during thermodynamic processes and is used to relate pressure drops, volume changes, and temperature variations in the analysis of ideal gasses.

Internal Energy of an Ideal Gas

For an ideal gas, the internal energy is dependent solely on the temperature of the gas. Therefore, any change in temperature results in a corresponding change in internal energy, regardless of how the process occurs. This relationship is critical when applying the first law of thermodynamics to determine the internal energy change in various thermodynamic processes.

Constant Pressure Process

A constant pressure process is one in which the system’s pressure remains constant while the volume may change. The work done during such a process is calculated as the product of the constant pressure and the change in volume (W = P?V), which is essential in quantifying energy transfer in processes where expansion or compression occurs at steady pressures.

First Law of Thermodynamics

This principle states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system (?U = Q - W). It is a statement of energy conservation and is the foundational principle behind analyzing energy transfers in any thermodynamic process, including multi-step processes such as constant volume cooling followed by constant pressure expansion.

Constant Volume Process

In a constant volume process, the volume of the gas remains fixed while other state variables such as pressure and temperature may change. Since the volume does not change, no work is done by or on the system (W = 0), making it easier to determine changes in internal energy and heat transfer solely from temperature changes.

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