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songoku
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Homework Statement
A cylinder is equipped with a smoothly movable piston which is connected by a spring to the bottom of the cylinder as shown in the figure. An ideal gas of 0.1 mol is confined in the space on the left side of the cylinder at a temperature of 300 K. The atmospheric pressure is 1 x 105 Pa. Take the cross-section area of the piston to be 1 x 10-3 m2, the spring constant to be 500 N/m and the gas constant to be 8.3 J / mol K
1. Initially the spring is at its natural length. Calculate the volume of the gas
By heating the gas, the piston moves to the right a distance of 0.2 m
2. Calculate the pressure of the gas after the change
3. Calculate the temperature of the gas after the change
4. Calculate the work done by the gas during the change
Homework Equations
W = p ΔV
PV / T = constant
F = kx
W = 1/2 kx2
The Attempt at a Solution
1. done (ans = 2.5 x 10-3 m3 )
2.
P = F/A = kx/A = (500) (0.2)/(1 x 10-3) = 1 x 105 Pa
but the answer is 2 x 105 Pa.
So should it be the initial pressure + P = 1 x 105 Pa + 1 x 105 Pa = 2 x 105 Pa ??
3. no problem if (2) done
4. work done = 1/2 kx2 = 1/2 (500) (0.2)2 = 10 J
but the answer is 30 J...don't know what to do and why I was wrong...
thanks