A rigid container has 1 kg CO2 at 300 K and 1 kg Ar at 400 K, both at 150 kPa. Now they are

step 1 The question is saying that they are allowed to mix without any heat transfer. So no Q, no W. So

A rigid container has 1 kg CO2 at 300 K and 1 kg Ar at...

A rigid container has $1 \mathrm{~kg} \mathrm{CO}_{2}$ at $300 \mathrm{~K}$ and $1 \mathrm{~kg}$ Ar at $400 \mathrm{~K}$, both at $150 \mathrm{kPa}$. Now they are allowed to mix without any heat transfer. What is the final $T, P ?$

Key Concepts

Ideal Gas Law

The ideal gas law (PV = mRT) relates pressure, volume, temperature, and the amount of a gas. It is fundamental to understanding the behavior of gases under different thermodynamic conditions and is used to determine properties like pressure or volume when the others are known.

Conservation of Energy in Adiabatic Processes

In adiabatic processes, there is no heat transfer between the system and its surroundings, meaning that any change in the internal energy of the system is solely due to work done on or by the system. For a rigid container where volume remains constant, no work is done, so the total internal energy of the gas mixture remains constant throughout the process.

Internal Energy Dependence on Temperature

For ideal gases, the internal energy is a function of temperature only and can be computed using the specific heat capacity at constant volume (Cv). This principle allows the calculation of the final equilibrium temperature when gases with different initial temperatures and masses mix in an isolated system.

Mixing of Gases in a Rigid Container

When gases in a rigid container mix without any heat transfer, the final equilibrium state is reached by conserving the total internal energy. The mixing process leads to a uniform temperature and pressure determined by the weighted contributions of each gas’s internal energy and the ideal gas law applied to the combined gas mixture.

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