18. How many gallons of gasoline must be burned in order to raise the temperature of 10 liters of water from 25o C to 50o C, assuming 50 percent efficiency in converting the heat released into heat in the water?(The heat of combustion of gasoline is 3.4 × 107 cal/gallon.) v = { (average speed) d = v,t + at? (distance under acceleration)W %3D mg (Weight) а %3Fact(Acceleration) F= Gm,m2(Gravity Law)(Kinetic Energy) PE=mgh (Potential Energy)p = mvW = F ·d (Work Done) Q= mcAT (Heat Energy) Q=mL (Latent Heat Energy)effciency =%3Dwork doneenergy provided

Answered: How many gallons of gasoline must be…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

18. How many gallons of gasoline must be burned in order to raise the temperature of 10 liters of water from 25^o C to 50^o C, assuming 50 percent efficiency in converting the heat released into heat in the water?

(The heat of combustion of gasoline is 3.4 × 10⁷cal/gallon.)

v = { (average speed) d = v,t + at? (distance under acceleration)
W %3D mg (Weight) а %3
Fact
(Acceleration) F= Gm,m2
(Gravity Law)
(Kinetic Energy) PE=mgh (Potential Energy)
p = mv
W = F ·d (Work Done) Q= mcAT (Heat Energy) Q=mL (Latent Heat Energy)
effciency =
%3D
work done
energy provided

Expert Solution

Step 1

Calculate the amount of heat to be absorbed by water to raise its temperature from T₁=25^o C to T₂=50^o C.

$\begin{array}{rcl} Q_{w} & = & m_{w} c ∆ T \\ = & m_{w} c (T_{2} - T_{1}) \\ = & (10 L \times \frac{1000 g}{1}) \times 4.184 J / g \cdot ° C \times (50 ° C - 25 ° C) \\ = & 1.046 \times 10^{6} J \times \frac{1 cal}{4.184 J} \\ = & 2.5 \times 10^{5} cal \end{array}$