To solve for the initial temperature of the gas in Kelvin and Celsius, we can use Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature in Kelvin when pressure is held constant. The formula is given as:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
Where:
- \(V_1\) = initial volume of the gas
- \(T_1\) = initial temperature of the gas in Kelvin
- \(V_2\) = final volume of the gas
- \(T_2\) = final temperature of the gas in Kelvin
We know:
- \(V_1 = 2.80 , \text{L}\)
- \(V_2 = 2.70 , \text{L}\)
- \(T_2 = 0.00 , \text{C} = 273.15 , \text{K}\)
We can rearrange the equation to solve for \(T_1\):
\[ T_1 = \frac{V_1 \times T_2}{V_2} \]
Now we can plug in the known values:
\[ T_1 = \frac{2.80 , \text{L} \times 273.15 , \text{K}}{2.70 , \text{L}} \]
Calculating this gives:
\[ T_1 = \frac{764.82}{2.70} \approx 283.2 , \text{K} \]
Next, converting \(T_1\) to Celsius:
\[ T_1 (\text{C}) = T_1 (\text{K}) - 273.15 \]
\[ T_1 (\text{C}) \approx 283.2 - 273.15 \approx 10.1 , \text{C} \]
So, the initial temperature of the gas is approximately:
- Temperature in Kelvin: 283.2 K
- Temperature in Celsius: 10.1 °C
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