# Ideal Gas Law

on . Posted in Thermodynamics

The ideal gas law can be used to predict pressuretemperature, and volume changes in ideal gasses.  An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.  In the real world, the ideal gas law must be corrected but it can serve as a good approximation for initial calculations.  The ideal gas law states that for a given amount of gas, the product of its pressure and volume is directly proportional to the number of moles of the gas and the absolute temperature.

The ideal gas law can be used to calculate various properties of ideal gases, such as finding the unknown pressure, volume, temperature, or number of moles if the other variables are known.  It is widely used in fields such as chemistry, physics, and engineering to analyze and predict the behavior of gases under different conditions.  It's important to note that the ideal gas law assumes idealized gas behavior, where the gas particles are considered point masses with no intermolecular forces and occupy negligible volume.  While real gases may deviate from ideal behavior under certain conditions, the ideal gas law is a useful approximation for many practical applications.

### Ideal Gas Law formula

$$p \; V = n \; R \; T$$     (Ideal Gas Law)

$$p = n \; R \; T \;/\; V$$

$$V = n \; R \; T \;/\; p$$

$$n = p \; V \;/\; R \; T$$

$$R = p \; V \;/\; n \; T$$

$$T = p \; V \;/\; n \; R$$

### Solve for p

 number of moles, n specific gas constant, R temperature, T volume, V

### Solve for V

 number of moles, n specific gas constant, R temperature, T pressure, p

### Solve for n

 pressure, p volume, V specific gas constant, R temperature, T

### Solve for R

 pressurt, p volume, V number of moles, n temperature, T

### Solve for T

 pressure, p volume, V number of moles, n specific gas constant, R

Symbol English Metric
$$p$$ = pressure of the gas $$lbf\;/\;in^2$$  $$Pa$$
$$V$$ = volume of the gas $$in^3$$ $$mm^3$$
$$n$$ = number of moles of gas $$dimensionless$$
$$R$$ = specific gas constant (gas constant) $$ft-lbf\;/\;lbm-R$$ $$J\;/\;kg-K$$
$$T$$ = temperature of the gas $$R$$ $$K$$

### notes

• Temperature is always the absolute temperature which will be either Rankine or Kelvin. For values that are in Fahrenheit, the conversion is °F - 459.67 = R. For values that are in Celsius the conversion is °C - 273 = K.
• Pressure is absolute pressure, not gauge pressure.
• Make sure units match on the universal gas constant.