A helium filled balloon has a volume of 2.75L at 20 celsius .The volume of the balloon decreases to 2.46L after it is placed outside on a cold day.What is the outside temperature in celsius?
A helium-filled balloon has a volume of 2.75 L at 20.0 °C. The volume of the balloon changes to 2.46 L when placed outside on a cold day. The temperature outside is
Answer : -10.9 °C
It’s -10.9 degrees celcious
answer
T₂=V₂T₁/V₁
To find the outside temperature in Celsius, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant for this problem)
V = volume of the balloon
n = number of moles of gas (constant for this problem)
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin:
Initial temperature (inside) = 20°C + 273.15 = 293.15 K
Final temperature (outside) = x°C + 273.15 = (x + 273.15) K
Now we can set up the equation using the initial and final volumes:
(P * 2.75) / 293.15 = (P * 2.46) / (x + 273.15)
Since the pressure (P), number of moles (n), and gas constant (R) are constant, they cancel out in this comparison.
Next, we can solve for x by cross multiplying:
2.75 * (x + 273.15) = 2.46 * 293.15
Simplifying the equation:
2.75x + 2.75 * 273.15 = 2.46 * 293.15
Now, let's solve for x:
2.75x = (2.46 * 293.15) - (2.75 * 273.15)
x = [(2.46 * 293.15) - (2.75 * 273.15)] / 2.75
By plugging in the values and calculating the equation, we can find the value of x, which represents the outside temperature in Celsius.