An aerosol can contains gases under a pressure of 4.5 atm at 27 ◦C. If the can is left on a hot sandy beach, the pressure of the gases increases to 4.85 atm. What is the Celsius temperature on the beach?
P1 = 4.50 atm
T1 = 27◦C +273 = 300 K
V1 = V2 = const
P2 = 4.85 atm
T2 = unknown
Solution:
Since the volume doesn't change, Gay-Lussac's Law can be used.
Gay-Lussac's Law can be expressed as: P1/T1 = P2/T2
P1T2 = P2T1
To find the final temperature, solve the equation for T2:
T2 = P2T1/P1
T2 = (4.85 atm × 300 K) / (4.50 atm) = 323.33 K = 323 K
T2 = 323 K or 323 - 273 = 50◦C
Answer: 50◦C
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