Answer :
The new temperature of the balloon if the volume is decreased to the given amount is 338.5K.
Charles's law
Charles's law states that the volume occupied by a definite quantity of gas is directly proportional to its absolute temperature.
It is expressed as;
[tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]
Given the data in the question;
- Initial volume; [tex]V_1 = 261L[/tex]
- Initial temperature; [tex]T_1 = 502K[/tex]
- Final volume; [tex]V_2 = 176L[/tex]
Final Temperature; [tex]T_2 = \ ?[/tex]
To determine the new temperature as the volume is decrease, we substitute our given values into the expression above.
[tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}\\\\V_1T_2 = V_2T_1\\\\261L * T_2 = 176L * 502K\\\\261L * T_2 = 88352L.K\\\\T_2 = \frac{88352L.K}{261L}\\ \\T_2 = 338.5K[/tex]
Therefore, the new temperature of the balloon if the volume is decreased to the given amount is 338.5K.
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