M Under constant pressure, the temperature of 2.00 mol of an ideal monatomic gas is raised 15.0

step 1 So we're given that the pressure doesn't change. And then we have two moles and now it changes b

M Under constant pressure, the temperature of 2.00 mol of...

M Under constant pressure, the temperature of $2.00 \mathrm{~mol}$ of an ideal monatomic gas is raised $15.0 \mathrm{~K}$. What are (a) the work $W$ done by the gas, (b) the energy transferred as heat $Q$, (c) the change $\Delta E_{\text {int }}$ in the internal energy of the gas, and (d) the change $\Delta K$ in the average kinetic energy per atom?

Key Concepts

First Law of Thermodynamics

This principle states that the energy of an isolated system is conserved; it relates the change in internal energy of a system to the heat added to the system and the work done by the system. It is fundamental in connecting energy transformations during thermodynamic processes.

Work Done Under Constant Pressure

When a gas expands or contracts at constant pressure, the work done by the gas is given by the product of the pressure and the change in volume. This concept is essential in calculating energy exchanges during isobaric processes, where pressure remains fixed while the temperature and volume change.

Internal Energy of an Ideal Monatomic Gas

For an ideal monatomic gas, the internal energy is solely a function of temperature and is given by a multiple of the temperature (typically (3/2)nRT for n moles). This concept highlights that the microscopic energy stored in the gas molecules is directly dependent on temperature, irrespective of the process path.

Heat Transfer in Constant Pressure Processes

The heat transferred into or out of a gas undergoing constant pressure change depends on the molar heat capacity at constant pressure. This determines how much energy is required to change the temperature of the gas, taking into account both the increase in internal energy and the work done during expansion or compression.

Average Kinetic Energy per Atom

In an ideal gas, the average translational kinetic energy of the atoms is directly proportional to the absolute temperature. This relationship links microscopic motion of the particles to the macroscopic property of temperature, thereby bridging molecular dynamics and thermodynamic behavior.

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