A house has well-insulated walls. It contains a volume of 90 m3 of air at 315 K.(a) Consider heating it at constant pressure. Calculate the energy required to increase the temperature of this diatomic ideal gas by 1.4°C. (b) If this energy could be used to lift an object of mass m through a height of 2.3 m, what is the value of m?

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Asked Sep 17, 2019
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A house has well-insulated walls. It contains a volume of 90 m3 of air at 315 K.

(a) Consider heating it at constant pressure. Calculate the energy required to increase the temperature of this diatomic ideal gas by 1.4°C.
 
(b) If this energy could be used to lift an object of mass m through a height of 2.3 m, what is the value of m?
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Step 1

Solution:

Given that the air is contained inside a house, the Pressure P of the gas can be taken equal to the atmospheric pressure.

The Ideal gas Equation is used for calculating the number of moles n of a diatomic gas (air) within the house.

The ideal gas equation is given by,

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PV nRT

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Step 2

Here V  is the volume of the diatomic gas(air) contained inside the house, R is the gas constant , n is the number of moles of the diatomic gas (air) and T is the initial Temperature of the diatomic gas.

Substitute 1.013 x 105 N / m2 for P, 90 m3 for V, (air), 8.314 J/ mole.K for R, 315 K for T  and solve for n as,

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1.013(10')(N/m2)(90 m') = n(8.314 J/mole K)(315K) 1.013(10)(N/m2)(90m') (8.314 J/mole K)(315K) n = 3481.22

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Step 3

The first law of thermodynamics for Work done on ...

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Q-Δυ+ W. cp

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