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# p-V-T diagram for ideal gases

### p-V-T diagram for ideal gases

The relationship between the pressure, volume and temperature of ideal gases is described by the gas laws.

Physics

Keywords

p-V-T diagram, ideal gas, gas laws, Boyle-Mariotte law, Gay-Lussac´s 1st law, Gay-Lussac´s 2nd law, P-v-T surface, isochoric process, isothermal process, isobaric process, value of a quantity, state quantity, thermodynamics, temperature, pressure, volume, gas, temperature change, volumetric thermal expansion, physical property, physics, physical

Related items

### p-V-T diagram

• p - Pressure
• V - Volume
• T - Temperature
• p ₁
• p ₂
• p ₃
• p ₄
• T ₁
• T ₂
• T ₃
• T ₄
• V ₁
• V ₂
• V ₃
• V ₄

### Constant temperature

• p - Pressure
• V - Volume
• T = constant

When we view the p-V-T diagram from the T axis, we see a two-dimensional p-V diagram which describes corresponding changes in the volume and pressure of the gas at a fixed temperature.

When the gas is compressed at a constant temperature, its pressure increases. To ensure this, the gas has to release heat while being compressed and absorb heat while expanding.

This change is described by the Boyle-Mariotte law: if the temperature remains constant, the pressure and volume of a given amount of gas are inversely proportional.

The process takes place along isotherms.

### Constant volume

• p - Pressure
• V = constant
• T - Temperature

When we view the p-V-T diagram from the V axis, we see a two-dimensional p-T diagram which describes corresponding changes in the pressure and temperature of the gas at a fixed volume.

When the gas is heated while its volume is unchanged, its pressure will increase. This change is described by Gay-Lussac´s 2nd law: if the volume remains constant, the pressure of a given amount of gas is in direct proportion to its temperature. The process takes place along isochors.

### Constant pressure

• p = constant
• V - Volume
• T - Temperature

When we view the p-V-T diagram from the p axis, we see a two-dimensional V-T diagram which describes corresponding changes in the temperature and volume of the gas at a fixed pressure.

When the gas is heated while the pressure remains unchanged, its volume will increase. This change is described by Gay-Lussac´s 1st law: if the pressure remains constant, the volume and temperature of a given amount of gas are directly proportional. The process takes place along isobars.

### p-V-T surface

Correlations between the pressure, volume and temperature of a given amount of ideal gas may be described in three-dimensional graphs showing the three thermodynamic quantities.
The possible equilibrium conditions determine a 3D surface. Ideal gases occur in states that are on this surface. Therefore, if the values of two of the quantities are known, the value of the third can be determined, for example the volume of the gas can be calculated if the temperature and pressure are known.

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