In a proton linear accelerator, a 8.6 proton current hits a target.
5.4×10^16 protons/second hit the target.
How much energy is delivered to the target each second if each proton has a kinetic energy of 26 MeV and loses all its energy in the target?
U = J/s
If the target is a 1.90kg block of copper, at what rate will its temperature increase if it is not cooled?
delta T/s = kg degrees/second
Convert MeV to Joules/proton and multiply that by 5.5*10^16 protons/s
That gives you the answer in watts (or J/s).
Watts divided by (mass * specific heat)
is the rate of temperature increase
You will need to look up the specific heat of copper.
To find the amount of energy delivered to the target each second, we can multiply the number of protons hitting the target per second by the kinetic energy of each proton.
Given:
Proton current = 8.6 A
Number of protons per second = 5.4 × 10^16 protons/second
Kinetic energy of each proton = 26 MeV
First, let's convert the proton current from amperes to protons per second. An ampere is defined as one coulomb of charge passing through a point in one second. Since each proton has a charge of 1.6022 × 10^-19 coulombs, we can determine the number of protons per second using the formula:
Number of protons per second = Proton current (A) / Charge of a proton (C)
Number of protons per second = 8.6 A / (1.6022 × 10^-19 C)
Next, we can calculate the energy delivered to the target per second:
Energy delivered to the target per second = Number of protons per second × Kinetic energy of each proton
Energy delivered to the target per second = (Number of protons per second) × (Kinetic energy of each proton)
Now, let's substitute the values from the given information into the formula and calculate:
Energy delivered to the target per second = (5.4 × 10^16 protons/second) × (26 MeV)
To convert 26 MeV to joules, we can use the conversion factor: 1 MeV = 1.6022 × 10^-13 Joules
Energy delivered to the target per second = (5.4 × 10^16 protons/second) × (26 × 1.6022 × 10^-13 J)
Finally, calculate the result:
Energy delivered to the target per second = 2.214 × 10^4 J/s
So, the energy delivered to the target each second is 2.214 × 10^4 J/s.
Now, let's move on to the second part of the question. We need to calculate the rate at which the temperature of a 1.90 kg block of copper increases if it is not cooled.
To do this, we can apply the equation for heat transfer:
Energy = mass × specific heat capacity × change in temperature
Rearranging the equation, we get:
Change in temperature per second = Energy delivered to the target per second / (mass × specific heat capacity)
Given:
Mass of the copper block = 1.90 kg
Specific heat capacity of copper = 390 J/kg°C (at room temperature)
Substitute the values into the equation and calculate:
Change in temperature per second = (Energy delivered to the target per second) / (mass × specific heat capacity)
Change in temperature per second = (2.214 × 10^4 J/s) / (1.90 kg × 390 J/kg°C)
Finally, compute the result:
Change in temperature per second = 2.85 × 10^-2 °C/s
Therefore, if the copper block is not cooled, its temperature will increase at a rate of 2.85 × 10^-2 °C per second.