# How many times is the weight of the air that fills the room in winter (7 ° С) more than its weight in summer

How many times is the weight of the air that fills the room in winter (7 ° С) more than its weight in summer (37 ° С)? The pressure is the same.

Clapeyron’s equation for indoor air in winter and summer (pressure P, volume V, mass of one mole of air M are unchanged):

PV = mzRTz / M (T – temperature, R – gas constant, m – air mass);

PV = mlRTl / M.

The left-hand sides of the equalities are the same, so we can write the equality of the right-hand sides:

mzRTz / M = mlRTl / M;

mzTz = mlTl;

Tz = 273 + 7 ° C = 280 K;

T = 273 + 37 ° C = 310 K.

mz = mlT / Tz = (ml * 310 K) / 280 K = 1.107ml.

Answer: The mass of air in the room in winter is 1.107 times more than in summer.

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