6) A man heats a balloon in the oven. If the balloon initially has a volume of 0.4 liters and a temperature of 20 0C, what will the volume of the balloon be after he heats it to a temperature of 250 0C?
Assuming the pressure of the balloon remains constant, we can use the following equation:
(V1/T1) = (V2/T2)
where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Plugging in the values given:
(0.4 L / 293 K) = (V2 / 523 K)
Solving for V2, we get:
V2 = 0.4 L x (523 K / 293 K) = 0.71 L
Therefore, the volume of the balloon will be 0.71 liters after it is heated to 250 0C.
Some students believe that teachers are full of hot air. If I inhale 2.2 liters of gas at a temperature of 180 C and it heats to a temperature of 380 C in my lungs, what is the new volume of the gas?
Assuming the pressure remains constant, we can use the following equation:
(V1/T1) = (V2/T2)
where V1 is the initial volume, T1 is the initial temperature, V2 is the final volume, and T2 is the final temperature.
Plugging in the values given:
(2.2 L / 453 K) = (V2 / 653 K)
Solving for V2, we get:
V2 = 2.2 L x (653 K / 453 K) = 3.18 L
Therefore, the new volume of the gas in your lungs is 3.18 liters.
To find the volume of the balloon after heating it to a higher temperature, you can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
To solve this problem, we need to convert the initial temperature and the final temperature from Celsius to Kelvin. The Kelvin temperature scale starts at absolute zero (0 K), where Celsius is 273.15 degrees lower. So, to convert Celsius to Kelvin, you add 273.15.
Given:
Initial volume, V1 = 0.4 liters
Initial temperature, T1 = 20°C + 273.15 = 293.15 K
Final temperature, T2 = 250°C + 273.15 = 523.15 K
Assuming the pressure remains constant, we can rearrange the ideal gas law equation to find the final volume (V2):
V2 = (nRT2) / P
Since the gas inside the balloon is the same, the number of moles (n) and the pressure (P) remain constant. Therefore, we can simplify the equation to:
V2 = (V1 * T2) / T1
Substituting the given values:
V2 = (0.4 * 523.15) / 293.15
Calculating this expression:
V2 ≈ 0.712 liters
Therefore, the volume of the balloon after heating it to a temperature of 250°C would be approximately 0.712 liters.