1. Thermo-physical properties 2. Radiation properties - nptel - Indian ...

Mechanical Measurements Prof S.P.Venkatesan
Indian Institute of Technology Madras
(This agrees with the value shown in Figure 5)
The heat conducted across the liquid layer is then given by
Q = Q − L= 29.91− 1.26 = 28.65 W
c e
Using Equation 2 the nominal value of the thermal conductivity of oil
sample is
−3
Qc
δ 28.65× 0.3× 10
k = = = 0.138 W / m° C
A θ 0.0133× 4.7
Now we calculate the uncertainty in the nominal value of the thermal
conductivity estimated above. Only the heat transferred and the
temperatures are susceptible to error. We know
2
V
thatQc
= Qe − L= − L.
Assuming that R is not susceptible to any
R
∂ Qc 2V2× 40 ∂Qc
error, we have = = = 1.495 W / V , = −1.
Hence the
∂V
R 53.5
∂L
error in the measured value of the heat conducted across the liquid layer
is
2 2
c c
⎛∂Q ⎞ ⎛∂Q ⎞
δQc=±
⎜ Δ V + ΔL
∂V ⎟ ⎜
∂L
⎟
⎝ ⎠ ⎝ ⎠
( ) ( )
2 2
=± 1.495× 0.5 + − 1× 0.05× 1.26 =± 0.75 W
The errors in the measured temperatures are equal and hence the error
in the measured temperature difference is
δθ =± 2Δ T =± 2 × 0.2 =± 0.283°
C.
The error propagation formula gives