If a hot air balloon has an initial volume of 1000 L at 70∘C, what is the temperature (in ∘C) of the air inside the balloon if the volume expands to 1900L ?
To find the temperature (in ∘C) of the air inside the balloon when the volume expands to 1900 L, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature if the pressure and number of moles remain constant.
The formula for Charles' Law is V₁ / T₁ = V₂ / T₂, where V₁ and T₁ are the initial volume and temperature, and V₂ and T₂ are the final volume and temperature.
Given:
Initial volume (V₁) = 1000 L
Initial temperature (T₁) = 70∘C
Final volume (V₂) = 1900 L
V₁ / T₁ = V₂ / T₂
Substituting the given values:
1000 L / 70∘C = 1900 L / T₂
To find T₂, we can cross-multiply:
1000 L * T₂ = 70∘C * 1900 L
Dividing both sides by 1000 L:
T₂ = (70∘C * 1900 L) / 1000 L
Calculating:
T₂ = 133000∘C / 1000 L
Simplifying:
T₂ = 133∘C
Therefore, the temperature of the air inside the balloon is 133∘C when the volume expands to 1900 L.
To determine the final temperature of the air inside the balloon when it expands to 1900 L, we can use the principle of Charles's Law. Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is constant.
To find the final temperature, we need to use the formula:
(V1/T1) = (V2/T2)
where:
V1 = initial volume = 1000 L
T1 = initial temperature = 70°C
V2 = final volume = 1900 L
T2 = final temperature (we need to find this)
We can rearrange the formula to solve for T2:
T2 = (V2 * T1) / V1
Now, let's substitute the given values into the formula:
T2 = (1900 * 70) / 1000
Calculating the equation:
T2 ≈ 133°C
Therefore, the temperature of the air inside the balloon, when its volume expands to 1900 L, is approximately 133°C.
(P1/T1) = (P2/T2)
Remember T must be in kelvin.