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2 years ago

12

Th e heat capacity of air is much smaller than that of water, and relatively modest amounts of heat are needed to change its tem

perature. Th is is one of the reasons why desert regions, although very hot during the day, are bitterly cold at night. Th e heat capacity of air at room temperature and pressure is approximately 21 J K−1 mol−1. How much energy is required to raise the temperature of a room of dimensions 5.5 m × 6.5 m × 3.0 m by 10°C? If losses are neglected, how long will it take a heater rated at 1.5 kW to achieve that increase given that 1 W = 1 J s−1?

2 answers:

LenKa [72]2 years ago

6 0

Answer:

The energy is 2.201x10⁴kJ and the time is 1.467x10⁴ s

Explanation:

please, the solution is in the attached Word file

Darina [25.2K]2 years ago

4 0

Answer:

Q=1005 J

t= 0.67 sec

Explanation:

Lets take condition of room is 1 atm and 25°C.

Heat capacity ,c = 21 J /K.mol

If we assume that air is ideal gas that

P V = n R T

$V= 5.5\times 6.5\times 3\ m^3$

$V=107.25\ m^3$

$V=107.25\times 1000 L$

V= 107250 L

At STP number of moles given as

$n=\dfrac{V}{V_{at\ S.T.P.}}$

V=22.4 L at S.T.P.

$n=\dfrac{107250}{22.4}\ moles$

n=4787.94 moles

n= 4.784 Kmoles

So heat required to raise 10°C temperature

Q = n x c x ΔT

Q = 4.78794 x 21 x 10

Q=1004.64 J

Time t

t= Q/P

P= 1.5 KW

t = 1.004.64 /1.5

t= 0.66 sec

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2 years ago

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Vladimir79 [104]

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