On hot days, you may have noticed that potato chip bags seem to “inflate”, even though they have not been opened. If I have a 250 mL bag at a temperature of 19 0C, and I leave it in my car which has a temperature of 600 C, what will the new volume of the bag be?
Assuming there is no change in the number of chips or the amount of air in the bag, we can use the Ideal Gas Law to determine the new volume of the bag:
PV = nRT
where:
P = pressure (assumed to be constant)
V = volume (what we're trying to find)
n = moles of gas (assumed to be constant)
R = gas constant (assumed to be constant)
T = temperature (in Kelvin)
We need to convert the temperatures to Kelvin:
19 0C = 292 K
60 0C = 333 K
Now we can set up the equation:
P(250 mL) = n(0.0821 L•atm/K•mol)(292 K)
P(new)V(new) = n(0.0821 L•atm/K•mol)(333 K)
Since n is constant, we can eliminate it from the equation:
P(250 mL) = P(new)V(new)(0.0821 L•atm/K•mol)(292 K)
V(new) = (P(250 mL))(292 K)/(P(new))(0.0821 L•atm/K•mol)(333 K)
We don't know the pressure, but we know that it increases as the temperature increases. So we can assume a higher pressure in the car, and use that to find an upper bound for the new volume:
V(new) ≤ (P(car))(250 mL)(292 K)/(P(car))(0.0821 L•atm/K•mol)(333 K)
V(new) ≤ 344 mL
So we can say that the new volume of the bag is approximately 344 mL. This increase in volume is due to the increased pressure of the air inside the bag, which results from the increase in temperature.