A balloon is filled with 3.4L of helium gas at 10.C. The temperature of the balloon increases to 50. C after being placed in a car on a sunny day. What is the final volume of the balloon? (assume that B is the saem as for air)
What is B?
To solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature (T1) = 10°C + 273.15 = 283.15 K
Final temperature (T2) = 50°C + 273.15 = 323.15 K
Next, we need to assume that the pressure (P) and the number of moles (n) remain constant. Therefore, we can rewrite the equation as:
P1V1/T1 = P2V2/T2
Given that the initial volume (V1) is 3.4 L, we need to solve for the final volume (V2).
Now, substituting the known values into the equation, we have:
P1 * 3.4 / 283.15 = P2 * V2 / 323.15
Since the pressure (P1) and pressure (P2) are the same, we can cancel them out:
3.4 / 283.15 = V2 / 323.15
To solve for V2 (the final volume), we multiply both sides by 323.15:
V2 = (3.4 / 283.15) * 323.15
Calculating this, we find:
V2 ≈ 3.89 L
Therefore, the final volume of the balloon is approximately 3.89 liters.