What Celsius temperature, T 2 , is required to change the volume of the gas sample in Part A (T 1 = 19 ∘ C , V 1 = 1.47×103L ) to a volume of 2.94×103L ? Assume no change in pressure or the amount of gas in the balloon.
To solve this problem, we can use Charles's Law, which states that when the pressure and the amount of gas are constant, the volume of a gas is directly proportional to its temperature in Kelvin (K).
Step 1: Convert the temperatures from Celsius to Kelvin. To convert Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
For the initial temperature, T1 = 19 °C:
T1(K) = 19 °C + 273.15 = 292.15 K
Step 2: Set up the equation using the ratio of volumes and temperatures. According to Charles's Law:
V1 / T1 = V2 / T2
V1 = 1.47 × 10^3 L
V2 = 2.94 × 10^3 L
T1 = 292.15 K (from step 1)
Substituting the values we have:
1.47 × 10^3 L / 292.15 K = 2.94 × 10^3 L / T2
Step 3: Solve for T2. To isolate T2, we can cross-multiply the equation:
(1.47 × 10^3 L) × T2 = (292.15 K) × (2.94 × 10^3 L)
1.47 × T2 = 292.15 × 2.94
1.47 × T2 = 857.151
T2 = 857.151 / 1.47
T2 ≈ 583.88 K
Step 4: Convert the temperature back to Celsius. Use the formula:
T(°C) = T(K) - 273.15
T2(°C) = 583.88 K - 273.15 = 310.73 °C
Therefore, the Celsius temperature required to change the volume of the gas sample to 2.94 × 10^3 L is approximately 310.73 °C.