Sustainable Energy
Sustainable Energy
1st Edition
ISBN: 9781133108689
Author: Richard A. Dunlap
Publisher: Cengage Learning
Question
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Chapter 9, Problem 1P
To determine

Find the time required to increase the oil temperature from 20°C to 100°C.

Expert Solution & Answer
Check Mark

Answer to Problem 1P

The time required to increase the oil temperature from 20°C to 100°C is 14.7sec¯.

Explanation of Solution

Given information:

The width of the parabolic trough l is 1.0m.

The insider diameter of the pipe d is 1cm.

Initial temperature T1 is 20°C  and the final temperature T2 is 100°C.

Calculation:

Take the mid day irradiance of incident radiation as 674W/m2 and incident power of the 1 m long parabolic trough P as 674 W.

The inside diameter of the pipe is 1 cm.

Find the volume of oil in a 1 m pipe section V.

V=π4d2×l=π41cm2×1m=π41cm×102m1cm2×1m=7.85×105m3

Take the density of oil ρ as 900kg/m3 and the value of specific heat C as 1,758J/kg°C.

Express the formula for energy Q as follows:

Q=mCΔT                                                                                                                   …... (1)

Here, the mass is m and the change in temperature is ΔT.

Write the expression for power P as follows:

P=QtQ=Pt

Here, t is the time required to raise the oil temperature.

The mass is the product of density and the volume. Therefore, m=ρV.

Substitute Pt for Q and ρV for m in equation (1).

Pt=ρVCΔTt=ρVCT2T1Pt=900kg/m3×7.85×105m3×1,758J/kg°C×100°C20°C674W

t=14.7sec

Therefore, the time required to raise the oil temperature is 14.7sec¯.

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