If the cylindrical pistons are 25.000 cm in diameter at 20.0 ∘c, what should be the minimum diameter of the cylinders at that temperature so the pistons will operate at 150.0 ∘c

Refer to the diagram shown below.

The piston supports the same load W at both temperatures.
The ideal gas law is

where
p = pressure
V = volume
n = moles
T = temperature
R = gas constant

State 1:
T₁ = 20 C = 20+273 = 293 K
d₁ = 25 cm piston diameter

State 2:
T₂ = 150 C = 423 K
d₂ = piston diameter

Because V, n, and R remain the same between the two temperatures, therefore


If the supported load is W kg, then

Similarly,




Because p₁/p₂ = T₁/T₂, therefore


The minimum piston diameter at 150 C is 20.8 cm.

20.8 cm diameter