The relationship between pressure, volume, temperature, and the number of moles of a gas is described by the Ideal Gas Law. This law states that the product of pressure and volume is directly proportional to the product of the number of moles and the absolute temperature. Mathematically, it is expressed as:...
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of the gas
- R is the ideal gas constant (8.314 J/mol·K)
- T is the absolute temperature of the gas in Kelvin
Analyzing the Changes
In this scenario, the temperature (T) is doubled (increased by 2 times) and the volume (V) is reduced to one-third (decreased 3 times). Let's analyze how this affects the pressure (P). Assuming the number of moles (n) of the gas remains constant, we can use the Ideal Gas Law to determine the change in pressure.
Initially, the equation is:
P₁V₁ = nRT₁
After the changes, the equation becomes:
P₂V₂ = nRT₂
We know that T₂ = 2T₁ and V₂ = V₁/3. Substituting these values into the second equation, we get:
P₂(V₁/3) = nR(2T₁)
Dividing the second equation by the first equation, we get:
(P₂(V₁/3))/(P₁V₁) = (nR(2T₁))/(nRT₁)
Simplifying the equation, we get:
P₂/3P₁ = 2
Therefore, the final pressure (P₂) is six times the initial pressure (P₁):
P₂ = 6P₁
Conclusion
When the temperature of a gas is increased by two times and its volume is decreased by three times, the pressure of the gas will increase six times. This is a direct consequence of the Ideal Gas Law, which describes the relationship between pressure, volume, temperature, and the number of moles of a gas. This principle has important applications in various fields, including engineering, chemistry, and physics.