A balloon with a radius of 20.0 m at 6.0 oC is heated to 32.0oC. Find the new volume.
V1=4πR³/3=4π20³/3=33510 m³
T1-279K
T2=305K
V1/T1 =V2/T2
V2=V1•T2/T1
To find the new volume of the balloon, 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
T is the temperature in Kelvin
Firstly, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is based on absolute zero, with 0 K being the lowest possible temperature. To convert from Celsius to Kelvin, we simply add 273.15 to the Celsius temperature.
So, the initial temperature of the balloon is 6.0 °C + 273.15 = 279.15 K.
The final temperature of the balloon is 32.0 °C + 273.15 = 305.15 K.
Now, let's assume that the balloon is filled with an ideal gas, so we can consider it as an ideal gas. Therefore, the initial and final pressures remain constant.
Given that the radius of the balloon is 20.0 m, we can find the initial volume using the formula for the volume of a sphere:
V_initial = (4/3) * π * r^3
= (4/3) * π * (20.0 m)^3
Now, we can calculate the new volume using the ideal gas law equation, with the initial and final temperatures:
V_initial * T_final = V_new * T_initial
Solving for V_new, we get:
V_new = (V_initial * T_final) / T_initial
Substituting the values into the equation:
V_new = [(4/3) * π * (20.0 m)^3 * 305.15 K] / 279.15 K
Calculating this equation will give us the new volume of the balloon after being heated to 32.0 °C.