Question

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)

Answer 1

`114.4^(\circ)\text{C}`

Step-by-step explanation:

`T_1` = Initial temperature =
`25^(\circ)\text{C}=25+273\ \text{K}`

`V_1` = Initial volume = 50 L

`T_2` = Final temperature

`V_2` = Final volume = 65 L

We have the relation

`(V_2)/(V_1)=(T_2)/(T_1)\\\Rightarrow T_2=(V_2)/(V_1)* T_1\\\Rightarrow T_2=(65)/(50)* (25+273)\\\Rightarrow T_2=387.595\ \text{K}=387.4-273\\\Rightarrow T_2=114.4^(\circ)\text{C}`

The final temperature of the system would be
`114.4^(\circ)\text{C}`.