Final answer:
To find the temperature increase of the fluid per meter of pipe over 1 minute, we need to calculate the heat transfer using the equation Q = mc ∆T. By finding the mass of the mineral oil in the one-meter section of pipe, we can determine the heat transfer. Converting the temperature change from Fahrenheit to Celsius and dividing it by the length of the pipe will give us the temperature increase per meter.
Step-by-step explanation:
The increase in temperature is given by Q = mc ∆T. The mass m of the mineral oil in the one-meter section of pipe is determined by its density, which is approximately constant.
Therefore, we can write m = ρV, where ρ is the density and V is the volume of the mineral oil. Since the tube has a diameter of 2.00 cm, its radius is 1.00 cm or 0.01 m. The volume V of the mineral oil in the one-meter section of pipe is determined by its cross-sectional area A and its length L, which is 1.00 m.
Therefore, we can write V = AL. Since the cross-sectional area A of the pipe is given by A = πr², where r is the radius of the pipe, we can substitute the values given and calculate the cross-sectional area A.
Once we have the cross-sectional area A and the mass m, we can calculate the heat transfer Q using the equation Q = mc ∆T. The change in temperature ∆T is given as 30.0 °F/min. In order to determine the temperature increase per meter of pipe over a period of 1 minute, we need to convert this temperature change from Fahrenheit to Celsius, as the other values in the equation are in SI units.
Once we have the temperature change in Celsius per minute, we can divide it by the length of the pipe, which is 1.00 m, to obtain the temperature increase per meter of pipe over a period of 1 minute.