The heat capacity of air is much smaller than that of liquid water, and relatively modest amounts of heat are therefore needed to change the temperature of air. This is one of the reasons why desert r

Question

The heat capacity of air is much smaller than that of liquid water, and relatively modest amounts of heat are therefore needed to change the temperature of air. This is one of the reasons why desert regions, though very hot during the day, are bitterly cold at night. The molar heat capacity of air at 298 K and 1.00 atm is approximately $21 J K^{- 1} mol^{- 1}$ . Estimate how much energy is required to raise the temperature of the air in a room of dimensions $5.0 m \times 8.2 m \times 2.98 m$ by $1 0^{\circ} C$ .

Options:

Answer:

B

Solution:

$n_{air} = \frac{P . V}{RT}$

$= \frac{1.0 \times ( 5.0 \times 8.2 \times 2.98 ) \times 1 0 ^{3}}{0.082 \times 298} = 5000$

Now, $q = n . C_{m} .Δ T$

$= 5000 \times 21 \times 10 = 1.05 \times 1 0^{6} J = 1050 k J$

TestHub · Accepted Answer

n air ​ = RT P . V ​ = 0.082 × 298 1.0 × ( 5.0 × 8.2 × 2.98 ) × 1 0 3 ​ = 5000 Now, q = n . C m ​ .Δ T ​ = 5000 × 21 × 10 ​ = 1.05 × 1 0 6 J ​ = 1050 k J ​

Chemistry - Thermodynamics - I Question with Solution | TestHub

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