How much heat is required to raise the temperature of the air in a sealed room (

Question

How much heat is required to raise the temperature of the air in a sealed room (a cube of constant 3.2 m on a side) from 15 degree C to 25 degree C? Assume that air is entirely N_2 (molecular weight 28) and that the air pressure starts at p_0 = 0.97*10^5 Pa. Heat = J Air isn't really pure nitrogen. It is approximately 78.5% N_2 and 21.5% O_2 (molecular weight 32) by volume. (Ignore the other gasses, mostly argon.) How much heat is required in this case? Heat = J What is the heat capacity of the air in the sealed room? C_v = J/K What is the pressure of the oxygen gas in the room after it has been been heated to 25 degree C? Poxygen = Pa

Explanation / Answer

PV= NkT

a) 0.07 x 10^5 ( 3.20^3) = nK( 15+273)

nK = 7 x 10^3 ( 32.768)/ 288 = 796. 44

5/2 NK = 1991

Q( heat required) = 5/2 NK ( change in temp) = 1991 ( 283) = 563453 J apprx

b)) Heat will be saem as heat is not dependent on the composition of air

c) Cv= 1991

d) P(i)*((273+Tf)/(273+Ti)) *.215
(0.79 x 10^5) ( 273+ 25)/( 273+ 15)
0.817 x 10^5 Pa ( 21.5/100) = 17565.5 Pa apprx

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