Question

23. Challenge: A gas is heated so that it expands from a volume of 1.0L to a volume of 1.5 l. If the

initial temperature of the gas was 5.0°C, then what is the final temperature of the gas?

Answer 1

To calculate the final temperature of an expanding gas, you can use Charles's Law, which relates volume and temperature. By substituting the given values into the Charles's Law equation and solving for the final temperature in Kelvin, and then converting it to Celsius, you can find the final temperature of the gas.

Step-by-step explanation:

To find the final temperature of a gas that has expanded, we can use Charles's Law. This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin) increases or decreases. The formula is: V1/T1 = V2/T2, where V is volume and T is temperature (in Kelvin).

The initial volume (V1) is 1.0L, and the final volume (V2) is 1.5L. The initial temperature (T1) is 5.0°C, which is 278.15K. To find the final temperature in Kelvin (T2), rearrange the formula to get T2 = V2*T1/V1. Substituting in the values gives T2 = (1.5L * 278.15K) / 1.0L. Calculating this gives us a value for T2. To convert T2 back to Celsius, subtract 273.15 from the Kelvin temperature.

Answer 2

417 K is the “final temperature” of the gas.

Explanation:

According to “Charles law” the change in “volume” of a given mass of gas expanded is “directly proportional” to the “temperature” of the given gas expanded. When we keep “pressure” of the gas as constant. Mathematically,

`v \alpha T`

`(v)/(T)=\text { constant }`

If gas is expanded from initial volume to final volume and initial temperature to final temperature then,

`(v_(1))/(T_(1))=(v_(2))/(T_(2))`

`\begin{array}{l}{\text { Where, } v_(1) \text { and } v_(2) \text { are the initial and final volumes of the gas expanded recpectively,}} \\ {T_(1) \text { and } T_(2) \text { are the initial and final temperatures of the gas expanded recpectively }}\end{array}`

Given that,

Initial volume is 1.0L

Final volume is 1.5L

`\text { Initial temperatureis } 5.0^(\circ) \mathrm{C}=5+273=278 \mathrm{K}`

To find final temperature of the gas

Substitute the given values,

`(1)/(278)=(1.5)/(T_(2))`

`T_(2)=1.5 * 278`

`T_(2)=417 K`

Therefore, final temperature of the gas after expanding is 417 K.