To calculate the change in pressure when a gas is cooled, we can use the ideal gas law, which states:
PV = nRT
Where: P is the pressure of the gas V is the volume of the gas n is the number of moles of gas R is the ideal gas constant T is the temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin: Initial temperature (T1) = 100 °C + 273.15 = 373.15 K Final temperature (T2) = 10 °C + 273.15 = 283.15 K
Now, let's assume that the volume (V), the number of moles (n), and the ideal gas constant (R) remain constant. In that case, we can express the relationship between the initial and final pressures as:
P1 / P2 = T1 / T2
Plugging in the values:
P1 / P2 = 373.15 K / 283.15 K
Now, let's solve for the final pressure (P2):
P2 = P1 * (T2 / T1) = 60 Pa * (283.15 K / 373.15 K)
Calculating this expression gives us:
P2 = 45.08 Pa
Therefore, if 60 Pa of gas is cooled from 100 °C to 10 °C, the final pressure would be approximately 45.08 Pa.