Exploring an Expandable Gas Cylinder

[Touchme]

Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 6.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.


I searched for a similar question however I didnt understand it. Maybe it was the calculation error. Someone help me...

Homework Equations

PV = nRT
[PV/T]i = [PV/T]f
Volume of cylinder = Ah

The Attempt at a Solution

First I convert my units. Initial state: 101325 Pa, 293 K, and 0.006 m^3
I determined the constant by using the gas law PV/T. (101325)(0.006)/293 = 2.0749 [(Nm^2)/K].
After the temperature is increased to 503 K (273+230), the piston rises and the volume changes. The new volume is 0.006 + Ah = 0.006 + 0.01h. The pressure is equal to P = F/A. F is the force constant times dispalcement (h), which is 2000 N/m. P = 2000/0.01 = 200000h N/m^2.
Putting everything together we get
2.0749 = (200000h)(0.006+0.01h)/503

The answer h = 0.482 m or 48.2 cm is incorrect. Any suggestion or corrections. Thank you.

 

[Andrew Mason]

Homework Statement

An expandable cylinder has its top connected to a spring with force constant 2.00 103 N/m. (See Fig. P10.58.) The cylinder is filled with 6.00 L of gas with the spring relaxed at a pressure of 1.00 atm and a temperature of 20.0°C.I searched for a similar question however I didnt understand it. Maybe it was the calculation error. Someone help me...

Homework Equations

PV = nRT
[PV/T]i = [PV/T]f
Volume of cylinder = Ah

The Attempt at a Solution

First I convert my units. Initial state: 101325 Pa, 293 K, and 0.006 m^3
I determined the constant by using the gas law PV/T. (101325)(0.006)/293 = 2.0749 [(Nm^2)/K].
After the temperature is increased to 503 K (273+230), the piston rises and the volume changes. The new volume is 0.006 + Ah = 0.006 + 0.01h. The pressure is equal to P = F/A. F is the force constant times dispalcement (h), which is 2000 N/m. P = 2000/0.01 = 200000h N/m^2.
Putting everything together we get
2.0749 = (200000h)(0.006+0.01h)/503

The answer h = 0.482 m or 48.2 cm is incorrect. Any suggestion or corrections. Thank you.

You have to develop the equation for pressure:

$$P_f = P_i + kh/A = nRT_f/V_f$$

Since $P_i = nRT_i/V_i$, and $V_f = V_i + Ah$

you should be able to work that out for h.

AM

 

[kyle8921]

I would suggest double-checking your calculations and units to ensure accuracy. It is also important to consider the ideal gas law and how it applies to the situation. Additionally, it may be helpful to draw a diagram to visualize the problem and see if there are any other factors that need to be taken into account. If you are still having trouble, I recommend seeking guidance from a teacher or classmate for further assistance.