A gas is confined to a steel tank with a fixed volume. At 293 Kelvin (K), the gas exerts a pressure of 5.0 atmosphere (atm). After heating the tank, the pressure of the gas increases to 10.0 atm. What is the temperature of the heated gas?
Question
A gas is confined to a steel tank with a fixed volume. At 293 Kelvin (K), the gas exerts a pressure of 5.0 atmosphere (atm). After heating the tank, the pressure of the gas increases to 10.0 atm. What is the temperature of the heated gas?
Solution
To solve this problem, we can use the Gay-Lussac's law which states that the pressure of a gas is directly proportional to its temperature if the volume and the amount of gas are kept constant. The formula for Gay-Lussac's law is P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Given in the problem: P1 = 5.0 atm T1 = 293 K P2 = 10.0 atm We need to find T2.
Substitute the given values into the formula:
5.0 atm / 293 K = 10.0 atm / T2
To solve for T2, cross multiply and divide:
T2 = (10.0 atm * 293 K) / 5.0 atm
T2 = 586 K
So, the temperature of the heated gas is 586 Kelvin.
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