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frez [133]
3 years ago
7

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
Physics
1 answer:
Wittaler [7]3 years ago
3 0

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.

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