Suppose you take and hold a deep breath on a chilly day, inhaling 3.0 L of air a

Question

Suppose you take and hold a deep breath on a chilly day, inhaling 3.0 L of air at 0 degrees C . Assume that air pressure is 1.0atm . How much heat must your body supply to warm the air to your internal body temperature of 37degrees celcius ? How much does the volume of the air increase as it is warmed?

Explanation / Answer

a/ Q = n·cp·?T ?T = 37°C - (-10°C) = 47°C = 47K Molar heat capacity of dry air is [1]: cp = 29.07 Jmol?¹K?¹ Number of moles can be found using ideal gas law p·V = n·R·T => n = p·V/(R·T) = 101325Pa · 4×10?³m³ / ( 8.314472 Pam³mol?¹K?¹ · 263.15K) = 0.18524 mol => Q = 0.18524mol · 29.07 Jmol?¹K?¹ · 47K = 253J b/ Use ideal gas law p·V/T = n·R = constant => p1·V1/T1 = p2·V2/T2 => V2 = V1 · (p1/p2) · (T2/T1) = 4.0L · (1atm/1atm) · ( (37+ 273)K / (-10 + 273)K) = 4.7L

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