In the process from point b to point c, the gas in the engine is heated to a higher temperature. As the gas is heated, it expands pushing the syringe piston up. Let's assume that this process is isobaric. The temperature of the gas at point b is 20.2 ° C, and the gas temperature at point c is 60 ° C. If the diameter of the syringe piston is 1 cm and the volume of the gas at point b is 27.8 cm3, how much will the piston be pushed up at point c compared to its height at point b?

Been up all night. I Give up

I tried doing it this way.
V(r)=2*r^2*pi*(h-h1)
V = 2*r^2*pi*h
V= V(r) + V(r)*ΔT/273.15

V(r) being the change in volume. For some reason I keep coming up wrong.

I've gotten h1=.5627 cm but its wrong.
h=4.424 V(r)=94.56 ΔT=39.8 V=27.8

but like I said I'm wrong. =-(
Help plz

I'm sorry to hear that you're having trouble with this problem. Let's go through the steps together to find the correct answer.

First, let's identify the given values:
- The diameter of the syringe piston is 1 cm, which means the radius (r) is 0.5 cm.
- The volume of the gas at point b is 27.8 cm^3.
- The temperature at point b is 20.2 °C.
- The temperature at point c is 60 °C.

Now, to solve this problem, we can use the ideal gas law, which states that for an isobaric process (constant pressure), the relationship between the initial and final volumes and temperatures can be expressed as:

(V1 / T1) = (V2 / T2)

Let's denote the height of the piston at point b as h1 and at point c as h2.

We can calculate the initial height (h1) using the given volume (V1) and the formula for the volume of a cylinder:

V1 = π * r^2 * h1

Substituting the known values:

27.8 = π * (0.5)^2 * h1
27.8 = 0.25π * h1
h1 = 27.8 / (0.25π)
h1 ≈ 35.3 cm

Now, we need to find the final height (h2).

Using the ideal gas law, we can rearrange the equation to solve for V2:

V2 = (V1 * T2) / T1

Substituting the known values:

V2 = (27.8 * 60) / 20.2
V2 ≈ 82.18 cm^3

Next, we can use the volume of a cylinder formula to find the final height (h2):

V2 = π * r^2 * h2

Substituting the known values:

82.18 = π * (0.5)^2 * h2
82.18 = 0.25π * h2
h2 = 82.18 / (0.25π)
h2 ≈ 104.0 cm

Finally, to calculate how much the piston will be pushed up at point c compared to its height at point b, we subtract the initial height (h1) from the final height (h2):

h2 - h1 = 104.0 - 35.3
h2 - h1 ≈ 68.7 cm

Therefore, the piston will be pushed up approximately 68.7 cm compared to its initial height at point b.

I hope this helps! Let me know if you have any further questions.