A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a temperature of 20°C. What will the volume of the balloon be after he heats it to a temperature of 250°C?
initial temp = 273 +20 = 293
final temp = 273 + 250 = 523
P V = n R T
n is constant
R is constant
P is constant
so
V/T = n R / P = constant
so
0.4 / 293 = V / 523
so
V = (523 / 293) * 0.4 liters
To answer this question, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure remains constant.
Here's how you can calculate the volume of the balloon after it is heated to 250°C:
1. Convert the initial temperature from Celsius to Kelvin. To do this, add 273.15 to the temperature in Celsius.
Initial temperature = 20°C + 273.15 = 293.15 K
2. Convert the final temperature from Celsius to Kelvin.
Final temperature = 250°C + 273.15 = 523.15 K
3. Use the formula for Charles's Law:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume of the balloon (0.4 liters)
T1 = Initial temperature in Kelvin
V2 = Final volume of the balloon (unknown)
T2 = Final temperature in Kelvin
Plugging in the values:
0.4 L / 293.15 K = V2 / 523.15 K
4. Solve for V2 by cross-multiplying and dividing:
V2 = (0.4 L * 523.15 K) / 293.15 K
5. Calculate the result:
V2 ≈ 0.713 L
Therefore, the volume of the balloon after heating it to a temperature of 250°C will be approximately 0.713 liters.
To find the final volume of the balloon after heating it to 250°C, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming the pressure remains constant.
The equation for Charles's Law is:
V1/T1 = V2/T2
Where:
V1 = Initial volume of the balloon
T1 = Initial temperature of the balloon in Kelvin (20°C + 273.15 = 293.15 K)
V2 = Final volume of the balloon (what we are trying to find)
T2 = Final temperature of the balloon in Kelvin (250°C + 273.15 = 523.15 K)
Let's substitute the known values into the equation:
0.4 L / 293.15 K = V2 / 523.15 K
To solve for V2, we can cross-multiply and divide:
(0.4 L * 523.15 K) / 293.15 K = V2
V2 ≈ 0.712 L
Therefore, the volume of the balloon will be approximately 0.712 liters after heating it to a temperature of 250°C.