Answer :
To calculate the final pressure of an ideal gas cooled at constant volume, the combined gas law (P1/T1 = P2/T2) is used. By substituting the given initial pressure and temperatures converted to Kelvin into the formula, the final pressure is determined.
The student is asking about the change in pressure of an ideal gas as a result of a change in temperature at constant volume. To calculate the final pressure, we use the combined gas law which relates pressure, volume, and temperature of an ideal gas. The combined gas law can be expressed as P1/T1 = P2/T2, where P represents pressure, T represents temperature in Kelvin, and the subscript numbers 1 and 2 represent the initial and final states of the gas, respectively.
Let's apply this to the given problem:
- Initial pressure (P1) = 0.983 atm
- Initial temperature (T1) = 65.1
°C = 338.25 K (since K =
°C + 273.15) - Final temperature (T2) = 39.3
°C = 312.45 K
We'll use the combined gas law to compute the final pressure (P2).
P2 = P1 * (T2/T1)
Now substituting the given values:
P2 = 0.983 atm * (312.45 K / 338.25 K)
This yields the final pressure of the gas.