A tank contains 5 kg of air at an absolute pressure of 280 kPa and a temperature of 27^∘ C. If

step 1 Hello and welcome to this video solution of numerate. So the initial mass of air m1 that is equa

A tank contains 5 kg of air at an absolute pressure of 280...

A tank contains $5 \mathrm{~kg}$ of air at an absolute pressure of $280 \mathrm{kPa}$ and a temperature of $27^{\circ} \mathrm{C}$. If $1.5 \mathrm{~kg}$ of air is added to the tank and the temperature rises to $37^{\circ} \mathrm{C}$, determine the pressure in the tank.

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Key Concepts

Ideal Gas Law

This fundamental principle relates the pressure, volume, mass, and temperature of a gas. In the context of a fixed volume, the pressure in a tank can be directly derived from the mass and temperature of the contained air, using the relationship that pressure is proportional to the product of mass and absolute temperature. This law is essential in thermodynamics when analyzing changes in state variables of gases.

Closed System with Variable Mass

In problems involving tanks or confined spaces, the system is often considered closed, meaning the volume does not change. However, if additional mass is introduced into the system while other parameters vary (such as temperature), the changes in pressure become significant. Understanding how modifications in the mass of the gas, within the same fixed volume, affect pressure is crucial for solving these types of problems.

Absolute Temperature

Temperature must be expressed in an absolute scale, such as Kelvin, when applying gas laws like the ideal gas law. This is because the proportional relationships assume temperature is measured from absolute zero, ensuring that all thermodynamic calculations are accurate. Recognizing the need for and converting to absolute temperature is key in any problem involving gas laws.

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