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To what temperature Celsius must a 50-liter sample of methane at 25oC be heated in order to increase its volume to 65 liters? The pressure remains constant. (114oC)

Sagot :

boffeemadrid

Answer:

[tex]114.4^{\circ}\text{C}[/tex]

Explanation:

[tex]T_1[/tex] = Initial temperature = [tex]25^{\circ}\text{C}=25+273\ \text{K}[/tex]

[tex]V_1[/tex] = Initial volume = 50 L

[tex]T_2[/tex] = Final temperature

[tex]V_2[/tex] = Final volume = 65 L

We have the relation

[tex]\dfrac{V_2}{V_1}=\dfrac{T_2}{T_1}\\\Rightarrow T_2=\dfrac{V_2}{V_1}\times T_1\\\Rightarrow T_2=\dfrac{65}{50}\times (25+273)\\\Rightarrow T_2=387.595\ \text{K}=387.4-273\\\Rightarrow T_2=114.4^{\circ}\text{C}[/tex]

The final temperature of the system would be [tex]114.4^{\circ}\text{C}[/tex].

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