A jogger's internal energy changes because he performs 6.80 105 J of work and gives off 4.9 105 J of heat. However, to cause the same change in his internal energy while walking, he must do 8.10 105 J of work. Determine the magnitude of the heat given off while walking.
J
decrease in U = work done + heat given off
=(6.8 +4.9)*10^5
= 11.7 * 10^5 J
then
11.7*10^5 = 8.1*10^5 + heat given off
heat given off = (11.7-8.1)10^5 = 3.6*10^5 J
To determine the magnitude of the heat given off while walking, we need to use the first law of thermodynamics, which states that the change in internal energy (ΔE) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system:
ΔE = Q - W
In this case, the jogger's internal energy changes by ΔE while jogging and while walking. The given information states that:
ΔE_jogging = 6.80 x 10^5 J
ΔE_walking = ΔE_jogging
The work done while walking is:
W_walking = 8.10 x 10^5 J
Using the first law of thermodynamics, we can write the equation for both cases:
ΔE_jogging = Q_jogging - W_jogging
ΔE_walking = Q_walking - W_walking
Since ΔE_walking = ΔE_jogging, we can set these equations equal to each other:
Q_jogging - W_jogging = Q_walking - W_walking
Rearranging the equation:
Q_walking = Q_jogging - W_jogging + W_walking
Substituting the given values:
Q_walking = 6.80 x 10^5 J - 8.10 x 10^5 J + 4.9 x 10^5 J
Calculating:
Q_walking = 3.6 x 10^5 J
Therefore, the magnitude of the heat given off while walking is 3.6 x 10^5 J.
To determine the magnitude of the heat given off while walking, we need to use the principle of conservation of energy.
The principle of conservation of energy states that the total energy of an isolated system remains constant. In this case, the jogger and the walker are isolated systems. Therefore, the change in internal energy of the jogger and the walker would be the same.
The change in internal energy is given by the equation:
Change in internal energy = Work done + Heat added/removed
For the jogger:
Change in internal energy jogger = 6.80 x 10^5 J (work done) + 4.9 x 10^5 J (heat given off)
For the walker:
Change in internal energy walker = 8.10 x 10^5 J (work done) + Heat given off (to be determined)
Since the change in internal energy is the same for both cases, we can set the two equations equal to each other:
6.80 x 10^5 J + 4.9 x 10^5 J = 8.10 x 10^5 J + Heat given off
Simplifying the equation:
11.70 x 10^5 J = 8.10 x 10^5 J + Heat given off
Now, we can solve for the heat given off:
Heat given off = 11.70 x 10^5 J - 8.10 x 10^5 J
Heat given off = 3.60 x 10^5 J
Therefore, the magnitude of the heat given off while walking is 3.60 x 10^5 J.