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Given a sample of a gas at 21.0°c, at what temperature (in °c) would its volume be doubled? assume that the pressure remains constant.

Sagot :

SOLUTION:

Step 1: List the given values.

To convert the temperature from degree Celsius to kelvin, add 273.15 to the temperature expressed in degree Celsius.

[tex]\begin{aligned} & V_1 = V_1 \\ & T_1 = 21.0^{\circ}\text{C} = \text{294.15 K} \\ & V_2 = 2V_1 \end{aligned}[/tex]

Step 2: Calculate the final temperature (in degree Celsius) by using Charles' law.

To convert the temperature from kelvin to degree Celsius, subtract 273.15 from the temperature expressed in kelvin.

[tex]\begin{aligned} \frac{V_1}{T_1} & = \frac{V_2}{T_2} \\ T_2V_1 & = T_1V_2 \\ \frac{T_2V_1}{V_1} & = \frac{T_1V_2}{V_1} \\ T_2 & = \frac{T_1V_2}{V_1} \\ & = \frac{(\text{294.15 K})(2V_1)}{V_1} \\ & = \text{588.3 K} \\ & = \boxed{315.15^{\circ}\text{C}} \end{aligned}[/tex]

Hence, the volume of the gas would be doubled at 315.15°C.

[tex]\\[/tex]

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