A gas at 65degree c occupies 4.22l. What will be the volume of the gas at a temperature of 36.9degree c assuming constant pressure
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Step 1: Convert temperatures from Celsius to Kelvin.
To convert Celsius to Kelvin, add 273.15.
$$T_1 = 65 \, ^\circ\text{C} + 273.15 = 338.15 \, \text{K}$$
$$T_2 = 36.9 \, ^\circ\text{C} + 273.15 = 310.05 \, \text{K}$$
Step 2: Identify the given values.
Initial Volume ($V_1$) = $4.22 \, \text{L}$
Initial Temperature ($T_1$) = $338.15 \, \text{K}$
Final Temperature ($T_2$) = $310.05 \, \text{K}$
Final Volume ($V_2$) = ?
Step 3: Apply Charles's Law.
Charles's Law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature:
$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$
To find $V_2$, rearrange the formula:
$$V_2 = \frac{V_1 T_2}{T_1}$$
Step 4: Substitute the values and calculate $V_2$.
$$V_2 = \frac{(4.22 \, \text{L}) \times (310.05 \, \text{K})}{338.15 \, \text{K}}$$
$$V_2 = \frac{1308.411 \, \text{L} \cdot \text{K}}{338.15 \, \text{K}}$$
$$V_2 \approx 3.869 \, \text{L}$$
The volume of the gas at $36.9 \, ^\circ\text{C}$ will be approximately 3.87 L.
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