Question

A rigid tank whose volume is unknown is divided into two parts by a partition. one side of the tank contains an ideal gas at 927°c. the other side is evacuated and has a volume twice the size of the part containing the gas. the partition is now removed and the gas expands to fill the entire tank. heat is now applied to the gas until the pressure equals the initial pressure. determine the final temperature of the gas.

Answer 1

Answer is: temperature is 3600,45 K.
T₁ = 927°C + 273,15 = 1200,15 K.
V₂ = 2V₁.
V₃ = V₁ + V₂ = 3V₁; volume of entire tank.
p₁ = p₃.
T₃ = ?; temperature of entire tank.
The temperature-volume law (volume of a given amount of gas held at constant pressure is directly proportional to the Kelvin temperature):
V₁/T₁ = V₃/T₃.
V₁/T₁ = 3V₁/T₃.
T₃ = 3T₁.
T₃ = 3 · 1200,15 K = 3600,45 K.

Answer 2

Based on the volume of the entire tank and the temperature of the one side, the final temperature would be 3,327 ° C

Temperature of side with gas in Kelvin

= Temperature in Celsius + 273 kelvins

= 927 + 273

= 1,200 K

Final temperature

The volume of the entire tank will be three times the volume of the side with gas because the side without gas is twice the size of the side with gas:

= (2x volume) + volume

= 3 x volume

= ((3 x Volume of side with gas) x Temperature of side with gas ) / Volume of side with gas

= 3 x Temperature of side with gas

= 3 x 1,200

= 3,600 K

Final temperature in Celsius

= 3,600 k - 273 k

= 3,327 °C

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