An aerosol can contains gases under a pressure
of 4.5 atm at 15◦C. If the can is left on a
hot sandy beach, the pressure of the gases
increases to 4.78 atm. What is the Celsius
temperature on the beach?
Answer in units of ◦C
See four posts up.
sdvcdj
To solve this problem, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures given in Celsius to Kelvin. To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature.
15°C + 273.15 = 288.15 K (initial temperature)
T (in Kelvin) = 288.15 K
Next, let's solve for T (the final temperature). We know the initial pressure (P1), final pressure (P2), and the initial temperature (T1). We want to solve for T2 (final temperature).
P1 = 4.5 atm (initial pressure)
P2 = 4.78 atm (final pressure)
T1 = 288.15 K (initial temperature)
T2 = ? (final temperature)
We can rearrange the ideal gas law equation to solve for T2:
(P1 * V1) / T1 = (P2 * V2) / T2
Assuming the volume of the gas remains constant, we can cancel out V1 and V2:
P1 / T1 = P2 / T2
Now we can solve for T2:
T2 = (P2 * T1) / P1
Substituting the values:
T2 = (4.78 * 288.15) / 4.5
T2 ≈ 305.886 K
Finally, to convert the temperature back to Celsius, subtract 273.15 from T2:
305.886 K - 273.15 = 32.736°C
Therefore, the Celsius temperature on the beach is approximately 32.736°C.