Question

The properties of mercury at 300 K are: density = 13529 kg/m³, specific heat at constant pressure = 0.1393 kJ/kg-K, dynamic viscosity = 0.1523 × 10^-2 Ns/m² and thermal conductivity = 8.540 W/m-K. the Prandtl number of mercury at 300 K is:

1. 0.0248
2. 2.48
3. 24.8
4. 248

Answer 1

Correct Answer - Option 1 : 0.0248

Concept:

Prandtl number is the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{\nu }{\alpha } = \frac{μ }{{\frac{{ρ k}}{{ρ {C_p}}}}} = \frac{{μ {C_p}}}{k}\)

Calculation:

Given:

ρ = 13529 kg/m³, C_p = 0.1393 kJ/kg-K, μ = 0.1523 × 10^-2 Ns/m², k = 8.540 W/m-K

\(Pr = \frac{{μ {C_p}}}{k}\)

\(Pr = \frac{{0.1523\;\times\;10^{-2}\;\times\; {0.1393\;\times\;10^3}}}{8.540}=0.0248\)