Question

The label on aluminum aerosol can says temperature shouldn’t exceed 50*C. If the van is filled with ideal gas at 573 kPa at 20*C, what is the pressure (in ATM) at 50*C?

Answer 1

To solve this problem, we can use the ideal gas law, which states:

PV = nRT

Where: P is the pressure V is the volume n is the number of moles R is the ideal gas constant T is the temperature

We are given the initial conditions as follows: P₁ = 573 kPa T₁ = 20°C = 20 + 273.15 = 293.15 K

Let's assume the number of moles (n) and volume (V) remain constant. We can write the equation as:

P₁/T₁ = P₂/T₂

We need to find P₂ when T₂ = 50°C = 50 + 273.15 = 323.15 K.

Plugging in the values:

573 kPa / 293.15 K = P₂ / 323.15 K

Now, we can solve for P₂:

P₂ = (573 kPa / 293.15 K) * 323.15 K P₂ ≈ 632.46 kPa

To convert the pressure from kilopascals (kPa) to atmospheres (ATM), we can use the conversion factor:

1 ATM = 101.325 kPa

So, dividing the pressure by 101.325 kPa/ATM:

P₂ ≈ 632.46 kPa / 101.325 kPa/ATM P₂ ≈ 6.24 ATM

Therefore, the pressure at 50°C would be approximately 6.24 ATM.