A rigid tank contains a gas mixture with a specific heat of cy=0.748 kJ / kg ·K. The mixture is

A rigid tank contains a gas mixture with a specific heat of...

A rigid tank contains a gas mixture with a specific heat of $c_{y}=0.748 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}$. The mixture is cooled from $200 \mathrm{kPa}$ and $200^{\circ} \mathrm{C}$ until its pressure is $100 \mathrm{kPa}$. Determine the heat transfer during this process, in $\mathrm{kJ} / \mathrm{kg}$.

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Key Concepts

Rigid Tank (Constant Volume Process)

A rigid tank implies a process in which the volume remains constant throughout. This constraint means that no work is done by volume expansion or compression, and any change in the system’s energy is solely due to heat transfer.

First Law of Thermodynamics in Closed Systems

The first law of thermodynamics for a closed system states that the change in internal energy is equal to the heat added to the system minus the work done by the system. In a constant volume process, since no boundary work is performed, the net heat transfer directly changes the system's internal energy.

Specific Heat Capacity

Specific heat capacity is a measure of the amount of heat required to change the temperature of a unit mass of a substance by one degree Kelvin. It is a critical property for quantifying the relationship between energy transfer and temperature change in thermodynamic processes.

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and mass (or number of moles) of a gas. In processes where one or more of these properties change while others remain constant, the law is essential for predicting state changes as the system undergoes heating or cooling.

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