14. A sample of a monatomic ideal gas is originally at 20 °C. What is the final

Question

14. A sample of a monatomic ideal gas is originally at 20 °C. What is the final temperature of the gas if th pressure is doubled and volume is reduced to one-fourth its initial value? A) 900 °C B) 10°C C) 80°C D)-130°C E)-260°C 15. A bubble with a volume of 1.0 cm3 forms at the bottom of a lake that is 20.0 m deep. The temperature bottom of the lake is 10.0 °C. The bubble rises to the surface where the temperature is 25.0 °C. Assun the bubble is small enough that its temperature always matches that of its surroundings. What is the v of the bubble just before it breaks the surface of the water? A) 2.1 cm3 B) 2.8 cm3 C) 3.1 cm3 D) 6.0 cm3 B) 7.7 cm3

Explanation / Answer

Q14:

initial:

Vi = Vo; Pi = Po; Ti = 20 + 273 = 293 K

Final:

Pf = 2Po; Vf = Vo/4; Tf  = ?

combined gas law

Vi*Pi/Ti  = Vf*Pf/Tf

Vi*Pi*Tf  = Vf*Pf*Ti

Tf  = [Vf*Pf*Ti]/[Vi*Pi*] =  [Vo/4*2Po*293]/[Vo*Po*] = 293/2 K

Tf = 146.5K - 273K

Tf  = -126.5 oC = - 130 oC (Rounding off)

Answer:

Correct Choice is Option D.

Q15:

At the bottom:

V = 1.0 cm3;

p = po + gh

where po = 1.013*105 Pa, h = 20.0 m, = 1.0*103 kg/m3,

Therefore, p = 2.98*105 Pa

T = 10.0 + 273.2 = 283.2K

At the top:

V' = ?; p' = po; T' = 25.0 + 273.2 = 298.2K

using

pV/T = p'V'/T'

V' = V*(p/p')(T'/T) = 1.0 cm3*[2.98*105 Pa/1.013*105 Pa]*[298.2/283.2]

V' = 3.09 cm3

the volume of the bubble just before itbreaks the surface of the water is 3.1 cm3.

The Correct Option is 'C'

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