The volume of a gas is increased six times the original volume by heating it. If the original temperature of the gas was 27^circ C, what is the final temperature of the gas ? 1200^circ C 1800^circ C 1527^circ C 1500^circ C

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The volume of a gas is increased six times the original volume by heating it. If the original temperature of the gas was 27^circ C, what is the final temperature of the gas ? 1200^circ C 1800^circ C 1527^circ C 1500^circ C

Answer 1

### The final temperature of the gas is $1527^{\circ}C$.

Answer 2

## Step 1: Identify the Law The problem is about the relationship between the volume and temperature of a gas, which is described by Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its absolute temperature, assuming the pressure remains constant. ## Step 2: Use the Formula To find the final temperature, we can use the formula: \[\frac{V_1}{T_1} = \frac{V_2}{T_2}\] where $V_1$ is the initial volume, $T_1$ is the initial temperature, $V_2$ is the final volume, and $T_2$ is the final temperature. ## Step 3: Convert Temperature to Kelvin Given that $V_1$ is the original volume and $V_2$ is six times the original volume, and $T_1$ is $27^{\circ}C$, we need to convert this to Kelvin by adding 273.15, which gives: \[T_1 = 27 + 273.15 = 300.15 \text{ K}\] ## Step 4: Substitute Values and Solve Substituting the given values into the formula, we get: \[\frac{1}{300.15} = \frac{6}{T_2}\] Solving this equation for $T_2$, we get: \[T_2 = 6 \times 300.15 = 1800.9 \text{ K}\] ## Step 5: Convert Back to Celsius Finally, we convert this back to Celsius by subtracting 273.15 from $T_2$: \[T_2 - 273.15 = 1800.9 - 273.15 = 1527.75^{\circ}C\] which is approximately $1527^{\circ}C$. #

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The volume of a gas is increased six times the original volume by heating it. If the original temperature of the gas was 27^circ C, what is the final temperature of the gas ? 1200^circ C 1800^circ C 1527^circ C 1500^circ C

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