A sample of gas in a balloon has an initial temperature of 19 ∘ C and a volume of 1.47×103L . If the temperature changes to 63 ∘ C , and there is no change of pressure or amount of gas, what is the new volume, V 2 , of the gas?
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas sample when the pressure and amount of gas remain constant.
The combined gas law is represented as:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ and P₂ are the initial and final pressures of the gas (which remain constant),
V₁ and V₂ are the initial and final volumes of the gas,
T₁ and T₂ are the initial and final temperatures of the gas.
In this particular problem, the pressure and amount of gas are constant, so they do not affect the calculations. Therefore, we can simplify the equation to:
(V₁) / (T₁) = (V₂) / (T₂)
Now let's plug in the given values:
V₁ = 1.47 × 10³ L
T₁ = 19 °C (convert to Kelvin by adding 273) = 19 + 273 = 292 K
T₂ = 63 °C (convert to Kelvin) = 63 + 273 = 336 K
Now we have the equation:
(1.47 × 10³) / (292) = (V₂) / (336)
To find V₂, we can multiply both sides of the equation by 336:
(1.47 × 10³) / (292) * 336 = V₂
Let's calculate the value of V₂:
V₂ ≈ 1.682 × 10³ L
Therefore, the new volume of the gas, V₂, is approximately 1.682 × 10³ L.