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Sagot :
The final temperature is calculated to be 41.8 degrees Celcius if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa
The final temperature can be calculated by using the combined gas law as follows;
[tex]\frac{P_{1}V_{1} }{T_{1} } = \frac{P_{2}V_{2} }{T_{2} }[/tex]
Here [tex]P_{1}[/tex] and [tex]P_{2}[/tex] represent the initial and final pressure respectively,
[tex]V_{1}[/tex] and [tex]V_{2}[/tex] represent the initial and final volume respectively
[tex]T_{1}[/tex] and [tex]T_{2}[/tex] represent the initial and final temperature respectively
Converting [tex]T_{1}[/tex] to kelvin as follows;
[tex]T_{1}[/tex] = 27 degrees Celcius = 27 + 273 = 300 K
Now the final temperature can be determined by substituting the values in this equation of the combined gas law as follows;
(0.50×10^5)(1.25) / 300 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 = (0.82×10^5)(0.80) / [tex]T_{2}[/tex]
208.333333333 ([tex]T_{2}[/tex]) = (0.82×10^5)(0.80)
[tex]T_{2}[/tex] = (0.82×10^5)(0.80) ÷ 208.333333333
[tex]T_{2}[/tex] = 314.8 K
Converting K to degree Celcius as follows;
[tex]T_{2}[/tex] = 314.8 - 273 = 41.8 degree Celcius
Hence 41.8 degrees Celcius is calculated to be the final temperature.
Although a part of your question is incorrect, you might be referring to this question:
A cylinder fitted with a movable piston contains ideal gas at 27 degrees C, pressure 0.50*10^5 Pa, and volume 1.25 m^3. What will be the final temperature if the gas is compressed to 0.80 m^3 and the pressure rises to 0.82*10^5 Pa?
To learn more about temperature; click here:
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