Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
8th Edition
ISBN: 9780073398174
Author: Yunus A. Cengel Dr., Michael A. Boles
Publisher: McGraw-Hill Education
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Chapter 2.8, Problem 36P

(a)

To determine

The total power required to accelerate the car on the uphill road at a constant velocity.

(a)

Expert Solution
Check Mark

Answer to Problem 36P

The total power required to accelerate the car on the uphill road at a constant velocity is 47kW.

Explanation of Solution

The total work required to accelerate the car on the uphill road is equal to the summation of the rates of changes in kinetic and potential energies respectively.

Write the formula to calculate rate of change in kinetic energy of the car (W˙a).

W˙a=12m(V22V12)Δt (I)

Here, mass of the car is m, initial and final velocities of the car are V1 and V2 respectively and change in time interval is Δt.

Write the formula to calculate rate of change in potential energy of the car (W˙g).

W˙g=mgΔzΔt (II)

Here, acceleration due to gravity is g and change in vertical elevation of the car is Δz.

Write the formula to calculate total power required to accelerate the car on the uphill road (W˙total).

W˙total=W˙a+W˙g (III)

Conclusion:

Since the velocity is constant, the initial and final velocities of the car will be zero.

V=V1=V2=0

Then the rate of change in kinetic energy of the car will also be zero.

W˙a=0kW

Substitute 1150kg for m, 9.81m/s2 for g, 50m for Δz and 12s for Δt in Equation (II).

W˙g=(1150kg)(9.81m/s2)(50m)(12s)=(1150kg)(9.81m/s2)(50m)(12s)(1kJ1000kgm2/s2)=47kW

Substitute 0kW for W˙a and 47kW for W˙g in Equation (III).

W˙total=0kW+47kW=47kW

The total power required to accelerate the car on the uphill road at a constant velocity is 47kW.

(b)

To determine

The total power required to accelerate the car on the uphill road from rest to the final velocity.

(b)

Expert Solution
Check Mark

Answer to Problem 36P

The total power required to accelerate the car on the uphill road from rest to the final velocity is 90.1kW.

Explanation of Solution

Conclusion:

Substitute 1150kg for m, 30m/s for V2, 0m/s for V1 and 12s for Δt in Equation (I).

W˙a=12(1150kg)((30m/s)2(0m/s)2)(12s)=12(1150kg)((30m/s)2(0m/s)2)(12s)(1kJ1000kgm2/s2)=43.1kW

Substitute 43.1kW for W˙a and 47kW for W˙g in Equation (III).

W˙total=43.1kW+47kW=90.1kW

The total power required to accelerate the car on the uphill road from rest to the final velocity is 90.1kW.

(c)

To determine

The total power required to accelerate the car on the uphill road from initial to the final velocity.

(c)

Expert Solution
Check Mark

Answer to Problem 36P

The total power required to accelerate the car on the uphill road from initial to the final velocity is 10.5kW.

Explanation of Solution

Conclusion:

Substitute 1150kg for m, 5m/s for V2, 35m/s for V1 and 12s for Δt in Equation (I).

W˙a=12(1150kg)((5m/s)2(35m/s)2)(12s)=12(1150kg)((5m/s)2(35m/s)2)(12s)(1kJ1000kgm2/s2)=57.5kW

Substitute 57.5kW for W˙a and 47kW for W˙g in Equation (III).

W˙total=57.5kW+47kW=10.5kW

The total power required to accelerate the car on the uphill road from initial to the final velocity is 10.5kW.

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Chapter 2 Solutions

Thermodynamics: An Engineering Approach

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