Body temperature is about 308K. On a cold day, what volume of air at 273K must a person with a lung capacity of 2.00 L breathe in to fill the lungs?
(V1/T1) = (V2/T2)
Don't forget T must be in kelvin.
2.26
Oh, the temperature's dropping and lungs are expanding – it's like playing the balloon game with your body! Let's calculate how much air you need to fill those lungs.
Now, as we know, your body temperature is around 308K, while the air outside is chilly at 273K. It seems like you're aiming for a lung full of fresh, icy air!
To calculate the volume of air you'll need, we can use Charles's Law. Charles says that when the pressure remains constant, the volume of a gas is directly proportional to its temperature. So, we can set up a ratio with the two temperatures:
(Volume 1 / Temperature 1) = (Volume 2 / Temperature 2)
Now, let's plug in the values:
Volume 1 (lung capacity) = 2.00 L
Temperature 1 (body temperature) = 308K
Temperature 2 (cold air temperature) = 273K
(2.00 L / 308K) = (Volume 2 / 273K)
Now, let's solve for Volume 2, the volume of cold air you need:
Volume 2 = (2.00 L / 308K) * 273K
Calculating this gives us:
Volume 2 ≈ 1.76 L
So, to fill your lungs with that chilly air, you would need to inhale approximately 1.76 liters of it. Breathe it in, and enjoy the frosty freshness!
To find the volume of air a person needs to breathe in order to fill their lungs on a cold day, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure.
Given:
Initial temperature (T1) = 308 K
Initial volume (V1) = 2.00 L
Final temperature (T2) = 273 K (cold day)
Final volume (V2) = ?
We can set up the following equation using Charles's Law:
(V1 / T1) = (V2 / T2)
Substituting the given values:
(2.00 L / 308 K) = (V2 / 273 K)
To solve for V2, we can cross-multiply and then divide:
2.00 L × 273 K = V2 × 308 K
546 L·K = V2 × 308 K
Now, divide both sides of the equation by 308 K to isolate V2:
(546 L·K) / 308 K = V2
V2 ≈ 1.77 L
Therefore, a person with a lung capacity of 2.00 L needs to breathe in approximately 1.77 L of air at 273K to fill their lungs on a cold day.
To determine the volume of air that a person with a lung capacity of 2.00 L must breathe in to fill the lungs, we can use the ideal gas law. The ideal gas law relates the pressure (P), volume (V), temperature (T), and number of moles of gas (n). It can be written as:
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 (approximately 8.314 J/(mol·K))
T is the temperature of the gas in Kelvin
In this case, we have the temperature (T) of the air as 273K and the volume (V) of the lungs as 2.00 L. We are looking for the volume (V) of the air that needs to be breathed in. So we need to rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
To find the volume of air, we need to know the number of moles of air and the pressure. The pressure can vary, but assuming it is about atmospheric pressure (around 101325 Pa), we can focus on finding the number of moles.
To find the number of moles, we can use the ideal gas equation in the form of:
PV = nRT
We can rearrange this equation to solve for n:
n = PV / RT
Let's plug in the values given:
Pressure (P) = 101325 Pa (approximate atmospheric pressure)
Volume (V) = 2.00 L
Temperature (T) = 273 K
Ideal gas constant (R) = 8.314 J/(mol·K)
n = (101325 Pa * 2.00 L) / (8.314 J/(mol·K) * 273 K)
Now, we can calculate the number of moles of air.
n = 762.37 mol
Now, let's substitute the value of n back into the volume formula:
V = (nRT) / P
V = (762.37 mol * 8.314 J/(mol·K) * 273 K) / 101325 Pa
V ≈ 14.741 L (rounded to three decimal places)
Therefore, on a cold day with a lung capacity of 2.00 L, a person would need to breathe in approximately 14.741 liters of air to fill their lungs.