Question

A cylinder is closed by a piston connected to a spring of constant 1.60 103 N/m. With the spring relaxed, the cylinder is filled with 5.00 L of gas at a pressure of 1.00 atm and a temperature of 20.0

Answer 1

Answer:

The height is 0.247 m.

Explanation:

Given that,

Spring constant = 1.60\times10^3\ N/m[/tex]

Pressure = 1.00 atm

Temperature = 20.0°C

Suppose if the piston has a cross section area of 0.0120 m² and negligible mass, how high will it rise when the temperature is raised to 250°C

The equation of the pressure is

$P'=P_{0}+\dfrac{kh}{A}$...(I)

The equation of the volume is

$V'=V_{0}+Ah$....(II)

We need to calculate the height

Using equation of ideal gas

$\dfrac{P_{0}V}{T}=\dfrac{P'V'}{T'}$

$P'V'=P_{0}V\dfrac{T'}{T}$

Put the value of P' and V' from equation (I) and (II)

$P_{0}+\dfrac{kh}{A}\times V_{0}+Ah=P_{0}V\dfrac{T'}{T}$

Put the value into the formula

$1.013\times10^{5}+\dfrac{1.60\times10^{3}\times h}{0.0120 }\times5.00\times10^{-3}+0.0120 \times h=1.013\times10^{5}\times5.00\times10^{-3}\times\dfrac{523}{293}$

$1.013\times10^{5}\times5.00\times10^{-3}+1.013\times10^{5}\times0.0120\times h+1600h^2=904.09$

$1600h^2+1215.6h=904.09-506.5$

$1600h^2+1215.6h=397.59$

$h=0.247\ m$

Hence, The height is 0.247 m.