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jek_recluse [69]
3 years ago
12

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 te

mperature so the pistons will operate at 150.0 ∘c

Chemistry
1 answer:
attashe74 [19]3 years ago
8 0
Refer to the diagram shown below.

The piston supports the same load W at both temperatures.
The ideal gas law is
pV=nRT
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
\frac{p_{1}}{T_{1}} = \frac{p_{2}}{T_{2}}

If the supported load is W kg, then
p_{1} =  \frac{W \, N}{ \frac{\pi}{4} d_{1}^{2}} = \frac{4W \, N}{\pi (0.25 \, m)^{2}} =  20.3718W \, Pa
Similarly,
p_{2} =  \frac{4W}{\pi d_{2}^{2}} \, Pa

\frac{p_{1}}{p_{2}} =  \frac{20.3718 \pi d_{2}^{2}}{4} = 16 d_{2}^{2}

Because p₁/p₂ = T₁/T₂, therefore
16d_{2}^{2} =  \frac{293}{423}  \\\\ d_{2}^{2} =  \frac{0.6927}{16}  \\\\ d_{2} = 0.2081 \, m

The minimum piston diameter at 150 C is 20.8 cm.

Answer: 20.8 cm diameter

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