A jeweler is heating a gold bar. It takes 7 joules of heat
to raise the temperature of the bar 1°C. The initial
temperature of the bar is 25°C. Use this information
for Items 4–11.
4. Make a table that shows how many joules of heat
would be required to raise the temperature of the
gold bar to 26°C, 27°C, 28°C, 29°C, 30°C, and
35°C.
5. Write the equation of a function h(t) that
represents the amount of heat in joules required
to heat the bar to a temperature of t degrees
Celsius.
please explain step by step
so far i think im suppoesd to add 7 to 25 and keep going
That's right. For every additional °C, it takes 7 more Joules. So, your table looks like
°C J
26 7
27 14
28 21
...
h(t) = 7(t-25)
To find the amount of heat in joules required to raise the temperature of the gold bar to different temperatures, you need to use the given information that it takes 7 joules of heat to raise the temperature of the bar by 1 degree Celsius.
Let's start by finding the number of joules required to raise the temperature of the gold bar from 25°C to 26°C. Since it takes 7 joules to raise the temperature by 1°C, you would need to multiply 7 by the number of degrees you are raising the temperature, which is 1 in this case.
So, to raise the temperature from 25°C to 26°C, you would need 7 joules of heat.
Now let's continue this process to find the joules of heat required for each temperature increment. We can create a table to organize the calculations:
Temperature (°C) | Joules of Heat Required
---------------------------------------
26 | 7
27 | 14 (7 joules x 2)
28 | 21 (7 joules x 3)
29 | 28 (7 joules x 4)
30 | 35 (7 joules x 5)
35 | 70 (7 joules x 10)
To write the equation of a function h(t) that represents the amount of heat in joules required to heat the bar to a temperature of t degrees Celsius, you can use the formula:
h(t) = 7t
This equation simply states that the amount of heat required (h) is directly proportional to the temperature (t), with a proportionality constant of 7 joules/°C.
By substituting different values of t into the equation, you can easily find the amount of heat in joules required for any given temperature.
I hope this step-by-step explanation helps you understand how to calculate the joules of heat required and how to write an equation representing the amount of heat as a function of temperature. Let me know if you have any further questions!