Please answer all questions and show all work! 1. A gas fills the right portion

Question

Please answer all questions and show all work!

1. A gas fills the right portion of a horizontal cylinder whose radius is 6.00 cm. The initial pressure of the gas is 1.01 x 103 Pa. A piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the figure shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 23.0 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring. frictionless movable N/m Unstrained spring Pin 2. What is the average (ms) speed of the molecules of a helium gas at a temperature of 25 C? m/'s

Explanation / Answer

1) at constant temperature,

P*V = constant

P2*V2 = P1*V1

P2 = P1*(V1/V2)

= P1*(V1/(2*V1))

= P1/2

= 1.01*10^5/2 pa

Force exerted by the spring, F = P2*A

= (1.01*10^5/2)*pi*0.06^2

= 571 N

compression of the spring, x = 23 cm = 0.23 m

now use, F = k*x

k = F/x

= 571/0.23

= 2483 N/m <<<<<<<<<-------------------Answer

2)

given

T = 25 C

= 25 + 273

= 298 K

we know, molar mass of helium, M = 4 gram/mol

= 0.004 kg/mol

we know,

v_rms = sqrt(3*R*T/M)

= sqrt(3*8.314*298/0.004)

= 1363 m/s <<<<<<<<<-------------------Answer

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