Describe a scenario using the combined gas law in which changes occur in the pressure and temperature of an enclosed gas but the volume does not change.
Imagine a sealed container filled with a fixed amount of gas. Initially, the gas is at a pressure of 1 atm and a temperature of 273 K. Now, let's say we increase the temperature of the gas to 373 K while simultaneously decreasing the pressure to 0.5 atm.
According to the combined gas law (P1V1/T1 = P2V2/T2), since the volume of the gas is constant, we can rearrange the equation to solve for the unknown variables.
Using the given information:
P1 = 1 atm
T1 = 273 K
P2 = 0.5 atm
T2 = 373 K
V1 = V2 (volume does not change)
Now, plugging in the values into the equation:
(1 atm)(V1)/(273 K) = (0.5 atm)(V2)/(373 K)
By cross-multiplying and simplifying the equation, we find that the volume V1 is equal to the volume V2. This means that even though the pressure and temperature of the gas have changed, the volume remains constant. This scenario demonstrates the application of the combined gas law and how changes in pressure and temperature can affect the properties of a gas in an enclosed system.