In an air-conditioned room at 19.0 degree celsius , a spherical balloon had the diameter of 50.0cm . When taken outside on a hot summer day, the balloon expanded to 51.0cm in diameter. What was the temperature outside in degree celsius? Assume that the balloon is a perfect sphere and that the pressure and number of moles of air molecules remains the same.
The volume of a sphere is (4/3)*pi*r^3.
Knowing diameter calculate original volume. Use PV = nRT to calculate n. You don't have P but the problem states P is constant so just use a convenient number like 1 atm.
Then calculate new volume for expanded balloon, plug in everything but T and solve for new T.
Please don't cheat and use this website do your work and learn!
To find the temperature outside in degrees Celsius, we can use the ideal gas law, which states that the pressure (P), volume (V), and temperature (T) of a gas are related by the equation PV = nRT, where n is the number of moles of gas and R is the ideal gas constant.
In this case, we can assume that the pressure and number of moles of air molecules remains the same. Therefore, we can rewrite the equation as:
(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:
Diameter of the balloon in the air-conditioned room (V1) = 50.0 cm
Diameter of the expanded balloon outside (V2) = 51.0 cm
Temperature in the air-conditioned room (T1) = 19.0 degrees Celsius
First, we need to convert the diameters to volumes. The volume of a sphere is given by the formula: V = (4/3)πr^3
Where r is the radius of the sphere.
Let's calculate the initial volume (V1):
radius (r1) = diameter (D1) / 2 = 50.0 cm / 2 = 25.0 cm
V1 = (4/3)π(25.0 cm)^3
Next, let's calculate the final volume (V2):
radius (r2) = diameter (D2) / 2 = 51.0 cm / 2 = 25.5 cm
V2 = (4/3)π(25.5 cm)^3
Now, substitute the values into the equation:
(V1/T1) = (V2/T2)
((4/3)π(25.0 cm)^3)/(19.0 degrees Celsius) = ((4/3)π(25.5 cm)^3)/(T2 degrees Celsius)
Simplifying the equation:
(25.0 cm)^3 / 19.0 = (25.5 cm)^3 / T2
Solving for T2:
T2 = (25.5 cm)^3 * 19.0 / (25.0 cm)^3
Using a scientific calculator or a computer, evaluate the right-hand side of the equation to find T2. After substituting the values, you will find the approximate temperature outside in degrees Celsius.