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mit_hacker
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Homework Statement
Imagine you've been walking outside on an cold winter's day. When you arrive home at your studio apartment, you realize that you left a window open and your 5 {\rm m} \times 5 {\rm m} \times 3 {\rm m} room is only slightly warmer than the outside. You turn on your 1-kW space heater right away and wait impatiently for the room to warm up.
In this problem, make the following assumptions:
* The entire 1\;{\rm kW} = 1000\;{\rm J/s} output of the space heater goes into warming the air in the room.
* The air in the room is an ideal gas with five degrees of freedom per particle (three translational degrees of freedom and two rotational degrees of freedom--about right for nitrogen and oxygen).
* At room temperature and atmospheric pressure, one mole of air fills a volume of 23 liters. This is slightly larger than the volume of air at standard temperature and pressure, because room temperature is hotter than 0^\circ {\rm C}.
How long will it be before the heater warms the air in the room by 10 ^\circ {\rm C}?
Express your answer in minutes, to the nearest integer.
Homework Equations
Q=mc(T2-T1)
The Attempt at a Solution
the mass of air = 29g/mol = 0.029Kg/mol.
the volume is given to be 23 litres or 0.023m^3.
Therefore, density = 1.26
specific heat of air S = 1.0035 J g−1 K−1
mass of the air enclosed in the room = desity * volume
= 1.26 kg/m3 * 5m*5m*3m
m = 94.5 kg
heat reqiured to change the temperature of the room is
Q = mSΔT
= 94.5kg * 1003.5J kg−1 K−1 * 10 0
= 948307.5J
the power of the heater = 1kW
time reqiired = t = 903150J / 1000 J /sec
t = 948.3075 sec
In minuted to nearest integer, this is 16.
However, this is wrong.
What should the correct answer be?
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