(a) What is the initial volume of the air in the pump?2.63E-4m3(b) What is the number of moles of air in the pump?20.011mol(c) What is the absolute pressure of the compressed air?3Your response differs from the correct answer by more than 10%. Double check your calculations. Pa(d) What is the volume of the compressed air?4Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in yourcalculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. mi(e) What is the temperature of the compressed air?5K(f) What is the increase in internal energy of the gas during the compression?J Air (a diatomic ideal gas) at 25.0°C and atmospheric pressure is drawn into a bicycle pump (see figure below) that has a cylinderwith an inner diameter of 2.50 cm and length 53.5 cm. The downstroke adiabatically compresses the air, which reaches a gaugepressure of 8.00 x 10° Pa before entering the tire. We wish to investigate the temperature increase of the pump.

Name: (a) What is the initial volume of the air in the pump?2.63E-4m3(b) Wh
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Description: (a) What is the initial volume of the air in the pump?2.63E-4m3(b) What is the number of moles of air in the pump?20.011mol(c) What is the absolute pressure of the compressed air?3Your response differs from the correct answer by more than 10%. Doubl

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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(a) What is the initial volume of the air in the pump?
2.63E-4
m3
(b) What is the number of moles of air in the pump?
2
0.011
mol
(c) What is the absolute pressure of the compressed air?
3
Your response differs from the correct answer by more than 10%. Double check your calculations. Pa
(d) What is the volume of the compressed air?
4
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your
calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. mi
(e) What is the temperature of the compressed air?
5
K
(f) What is the increase in internal energy of the gas during the compression?
J

Air (a diatomic ideal gas) at 25.0°C and atmospheric pressure is drawn into a bicycle pump (see figure below) that has a cylinder
with an inner diameter of 2.50 cm and length 53.5 cm. The downstroke adiabatically compresses the air, which reaches a gauge
pressure of 8.00 x 10° Pa before entering the tire. We wish to investigate the temperature increase of the pump.

Expert Solution

Step 1

inner radius= 2.5cm/2=1.25cm=0.0125m

height = 53.5cm=0.535m

(a) The initial volume of the air pump= $2 {πr}^{2} h = 2 \times π \times {(0.0125)}^{2} \times 0.535 = 0.000525 m^{3}$

(b) Number of moles in the air pump: We know $P V = n R T, w h e r e R, t h e u n i v e r s a l g a s c o n \tan t = R = 8.314 J / m o l \cdot K 1 a t m = 101325 P a T = 25^{0} C = 298.15 k n = \frac{P V}{R T} = \frac{101325 \times 0.000525}{8.314 \times 298.15} = 0.0214 m o l e$

(d) The equation for adiabatic process is given by:

$P V^{γ} = C o n s \tan t T h e v a l u e o f γ f o r d i a t o m i c g a s i s \frac{7}{5}, ∴ P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ} \equiv V_{2} = V_{1} \times {(\frac{P_{1}}{P_{2}})}^{\frac{5}{7}} = 0.000525 \times {(\frac{101.325}{901.325})}^{\frac{5}{7}} = 0.00011 m^{3}$

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