Question

# An expandable cylinder has its top connected to a spring with force constant.

Other

An expandable cylinder has its top connected to a spring with force constant.
$$\displaystyle{2.00}\times{10}^{{3}}\ \frac{{N}}{{m}}$$. The cylinder is filled with 5.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of $$\displaystyle{20.0}^{\circ}$$

(a) If the lid has a cross-sectional area of 0.0100 $$\displaystyle{m}^{{2}}$$ and negligible mass, how high will the lidrise when the temperature is raised to T = 220°C?
(b) What is the pressure of the gas at 220°C?

2020-10-22
Ideal gas obey's all charle's laws and boyle's law.
Therefore
$$\displaystyle{P}_{{1}}\cdot{V}_{{1}}={P}_{{2}}\cdot{V}_{{2}}$$
and
$$\displaystyle{\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}={\frac{{{V}_{{2}}}}{{{T}_{{2}}}}}$$
Volume of the gas at $$\displaystyle{220}^{\circ}$$
$$\displaystyle{V}_{{2}}={\frac{{{V}_{{1}}}}{{{T}_{{1}}}}}\times{T}_{{2}}={\frac{{{5}}}{{{293}}}}\times{493}={8.41}$$
(b)The pressure of the gas at P$$\displaystyle{220}^{\circ}{C}$$
$$\displaystyle{P}_{{2}}={\frac{{{P}_{{1}}{V}_{{1}}}}{{{V}_{{2}}}}}={\frac{{{1}\times{5}}}{{{8.41}}}}={0.59}$$
Force acting on the piston
$$\displaystyle{F}={P}\times{A}={0.59}\times{101.325}\times{10}^{{3}}\times{0.01}$$
$$\displaystyle={597.81}$$ N
Displacement of the piston
$$\displaystyle{x}={\frac{{\text{Force}}}{{\text{force constant}}}}={\frac{{{F}}}{{{K}}}}={\frac{{{597.81}}}{{{2.00}\times{10}^{{3}}}}}={0.293}$$
$$\displaystyle{m}={29.3}{c}{m}$$