(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Q=mc(T2-T1)

3. 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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# Homework Help: Heating a room

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