We have this cylinder in our lab which contains 3g of oxygen and is fitted with

Question

We have this cylinder in our lab which contains 3g of oxygen and is fitted with a piston. The internal diameter of the cylinder is 8cm. On a fine Sunday morning, the graduate student fits a manometer into the cylinder and reads a gauge pressure of 300 kPa. Now the temperature and pressure in the lab are controlled to be at 20C and 1bar, respectively. The whole system is in equilibrium. a. Calculate the weight of the piston and the volume occupied by the gas. b. The graduate student supplies 100 Joules of heat to the cylinder and the piston rises by 5cm. Write the energy balance equation, remove terms that drop out, and calculate change in the internal energy of the cylinder contents before and after heating.

Explanation / Answer

The gauge pressure exists due to the weight of the piston.

Thus,

P = mpisg/A

or mpis= PA/g = 3,00,000 Pa x ( x 0.042)m2 / 9.8 m/s2

mass of piston = 153.769 kg

Weight put by piston = PA = 1507.96 N

B) U = Q + W

Q= 100 J

W= -PextV

Pext = 4 bar = 4 x 105 Pa

V = Ah = 2.513 x 10-4 m3

W= -100.53 J

U = -0.53 J

Internal energy decreases by 0.53 Joules

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