To calculate the change in volume of the air when the temperature increases while the pressure remains constant, we can use the ideal gas law. The ideal gas law states:
PV = nRT
Where: P = Pressure V = Volume n = Number of moles of gas R = Ideal gas constant T = Temperature in Kelvin
To solve the problem, we need to convert the temperatures from Celsius to Kelvin.
Initial temperature: T1 = 10°C + 273.15 = 283.15 K Final temperature: T2 = 30°C + 273.15 = 303.15 K
We can assume that the number of moles of air remains constant.
Now, let's calculate the initial and final volumes using the ideal gas law equation:
P1V1 = nRT1 P2V2 = nRT2
Since the number of moles (n) and the pressure (P) remain constant, we can write:
V1 / T1 = V2 / T2
Substituting the values:
V1 / 283.15 = V2 / 303.15
Now, let's solve for V2 (the final volume):
V2 = (V1 / T1) * T2
V2 = (2000 cu.m. / 283.15 K) * 303.15 K
V2 ≈ 2130.39 cu.m.
The change in volume is given by:
Change in volume = V2 - V1 Change in volume = 2130.39 cu.m. - 2000 cu.m. Change in volume ≈ 130.39 cu.m.
Therefore, when the temperature increases to 30°C while the pressure remains constant, approximately 130.39 cubic meters of air will be forced out of the room.