Question

Suppose you take and hold a deep breath on a chilly day, inhaling 2.4 L of air at 0∘C and 1 atm pressure. Assume that the air consists entirely of nitrogen and that the pressure of the gas stays constant as it warms to your core body temperature of 37∘C . by how much does the volume change?

Answer 1

The volume of air increases by about 0.32 L when it is inhaled at 0°C and warms to 37°C while at constant pressure, according to Charles's Law.

Step-by-step explanation:

To determine by how much the volume of air changes when it is inhaled at 0°C and exhaled at 37°C, we can use Charles's Law. Charles's Law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature (in Kelvin).

We first convert the temperatures from Celsius to Kelvin: T1 = 0°C = 273.15 K and T2 = 37°C = 310.15 K.

Using Charles's Law (V1/T1 = V2/T2), we can solve for the final volume V2:

• V1/T1 = V2/T2
• 2.4 L / 273.15 K = V2 / 310.15 K
• V2 = (2.4 L * 310.15 K) / 273.15 K

After calculating, we find that V2 is approximately 2.72 L. Therefore, the volume of air increases by about 0.32 L (2.72 L - 2.4 L) when it warms from 0°C to 37°C at constant pressure.

Answer 2

The volume of air increases by approximately 0.32 liters when 2.4 liters of air at 0°C warms up to the body's core temperature of 37°C at constant pressure.

Step-by-step explanation:

The question involves using the ideal gas law to calculate the change in volume when a gas changes temperature at constant pressure. This is a typical problem in thermodynamics, a branch of physics that deals with the relationship between heat, work, temperature, and energy. To solve for the change in volume, we can use Charles's law, which states that at constant pressure, the volume of a gas is directly proportional to its Kelvin temperature. The formula derived from Charles's law is:

V1/T1 = V2/T2

Given the initial conditions (V1 = 2.4 L, T1 = 273 K), and the final temperature (T2 = 310 K), we can solve for V2 as follows:

V2 = V1 * T2 / T1

V2 = (2.4 L) * (310 K) / (273 K)

V2 ≈ 2.72 L

The change in volume (ΔV) is:

ΔV = V2 - V1

ΔV ≈ 2.72 L - 2.4 L

ΔV ≈ 0.32 L

Therefore, the volume of air increases by approximately 0.32 liters when it warms to the body's core temperature.