Suppose we have 10x10x10cm closed box made of copper with air inside the box (ne

Question

Suppose we have 10x10x10cm closed box made of copper with air inside the box (neglect the thickness of the wall of the box). The box and the air inside are initially at 300k with pressure inside and outside at atmosphere 1.013x10^5Pa. The temp of the box and air inside is then raised to 400K constant P. a) calculate volume of the box at 300k and 400k copper @1.7x10^-5/k b)Calculate air molecules inside c)Calculate work done on the box by surrounding air while heated. d)Calculate pressure inside the box at 400k

Explanation / Answer

a) initially: Vi = 0.10^3 m^3 = 1 x 10^-3 m^3

finally: L = L0 (1 + alpha*deltaT)

L = 10 (1 + (1.7 x 10^-5 x 100)) = 10.017 cm Or 0.10017 m

Vf = L^3 = 1.0051 x 10^-3 m^3

b) using gas equation,

P V = n R T

(1.013 x 10^5) ( 10^-3) = n (8.314) (300)

n = 0.041 mol

c) Work done = 3 n R T / 2

    = (3 x 0.041 x 8.314 x (400-300))/2 = 51.13 J

d) P V / T = constant

(1.013 x 10^5) ( 1 x 10^-3) / (300) = P ( 1.0051 x 10^-3) / 400

P = 1.34 x 10^5 Pa

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