Answer:
Using the new cylinder the heat rate between the reservoirs would be 50 W
Explanation:
- Conduction could be described by the Law of Fourierin the form:
where 
is the rate of heat transferred by conduction, 
is the thermal conductivity of the material, 
and 
are the temperatures of each heat deposit, 
is the cross area to the flow of heat, and 
is the distance that the flow of heat has to go. - For the original cylinder the Fourier's law would be:
, and if 
, then the expression would be:
where 
is the diameter of the original cylinder, and 
is the length of the original cylinder. - For the new cylinder, in the same fashion that for the first, Fourier's Law would be:
,where 
is the heat rate in the second case, 
and 
are the new diameter and length. - But,
and 
, substituting in the expression for : 
. - Rearranging:
. - In the last declaration of , it could be noted that the expressión inside the parenthesis is actually
, then: 
. - <u>It should be noted, that the temperatures in the hot and cold reservoirs never change.</u>
<span>A.) If a sideways force of 300 N is applied to the motor, how far will it move sideways?</span>
Efficiency η of a Carnot engine is defined to be:
<span>η = 1 - Tc / Th = (Th - Tc) / Th </span>
<span>where </span>
<span>Tc is the absolute temperature of the cold reservoir, and </span>
<span>Th is the absolute temperature of the hot reservoir. </span>
<span>In this case, given is η=22% and Th - Tc = 75K </span>
<span>Notice that although temperature difference is given in °C it has same numerical value in Kelvins because magnitude of the degree Celsius is exactly equal to that of the Kelvin (the difference between two scales is only in their starting points). </span>
<span>Th = (Th - Tc) / η </span>
<span>Th = 75 / 0.22 = 341 K (rounded to closest number) </span>
<span>Tc = Th - 75 = 266 K </span>
<span>Lower temperature is Tc = 266 K </span>
<span>Higher temperature is Th = 341 K</span>
