Answer to Question #149243 in Mechanics | Relativity for Sudip

Question

A thermal tap used in certain apparatus consists of a silica rod which fits tightly
inside an Aluminium tube whose internal diameter is 8 mm at 0℃ . When the
temperature is raised, the fit is no longer exact. Calculate what change in temperature
is necessary to produce a channel whose cross-section is equal to that of a tube of
1 mm internal diameter

Answer 1

Let's T₁ = 273K, d₁ = 8mm, d₂ = 1mm;

we use the ideal gas law

PV/T = const

P₁V₁ / T₁ = P₂ V₂ / T₂

pressure is constant so

V₁ / T₁ = V₂ / T₂

$\pi$d₁² / 4T₁ = $\pi$d₂² / 4T₂

64 / T₁ = 1 / T₂

T_{2 =} T₁ / 64 = 273 / 64 = 4.23K;

the changing of temperature is that T₂ - T₁ = 268.67K;

the temperature decreasing to 268.67K