A thermocouple was calibrated to give Celsius temperature. In the ice bath the voltage reading was 0.250 V, and in boiling water at 736 Torr the reading was 1.20 V. Derive the conversion equation between Volts and temp. C.

So if I'm working this right, it should go like this:

0.0 degrees C= m(0.250mV) + b
100 degrees C= m(1.20mV) + b

b= (0.250mV)m

100 degrees C= (1.20mV)m + (0.250mV)m
m=100/(1.20+0.250)=
69.0 degrees C/mV

b=0.250m= 0.250x 69.0= 17.25

Temp. C=69.0E + 17.25

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And also for working basic conversions with sig figs such as:

A piece of metal measures 0.15m x 6 cm x 12mm If it weighs 486 g, what is its density in units g/cm3 and kg/dm3?

And temp. conversions: Given: -196*C = -321 *F, 77 K
And given 3.0 K= -454.4 *F, -270.2*C
And so on and so forth, my TA seems to always mark off for sig figs. I know for +/- the number of sig figs is the number with the least number of decimal places, and mult. and divide is the number with the least number of sig figs, but I never seem to record the right answer according to them, witch is really starting to confuse me because I don't see where I would be going wrong.

It appears to me you dropped a sign. Shouldn't the first calcn for b be

-b = (0.250 mV)m) and b is the negative of what you have.

Use William H. Seward's Speech at Sika, August 12,1869 to answer the question.

The speech encourages which of the following? Explain
A. colonialism
B. containment
C. imperialism
D. isolationism

I'm sorry, as an AI language model, I do not have personal beliefs or the ability to interpret speeches. However, I can provide you with information regarding the context of William H. Seward's Speech at Sika, August 12, 1869.

William H. Seward's Speech at Sika, August 12, 1869, was given during his travels as Secretary of State under President Andrew Johnson. In the speech, Seward discusses America's relationship with the world and advocates for a policy of expansion and increased international trade. He emphasizes the importance of the United States' role in the world and the benefits of connections with other nations.

Based on the content of the speech, it can be inferred that Seward's encouragement aligns with C. imperialism, as he advocates for the expansion of American influence and trade beyond its borders.

To derive the conversion equation between Volts and temperature in Celsius, you need to use the two data points given: the voltage reading in the ice bath (0.250 V) and the voltage reading in boiling water at 736 Torr (1.20 V).

First, set up two equations using the slope-intercept form of a linear equation (y = mx + b), where y represents temperature in Celsius and x represents voltage in volts:

Equation 1: 0.0 degrees C = m(0.250 V) + b
Equation 2: 100 degrees C = m(1.20 V) + b

To solve for the slope (m), subtract Equation 1 from Equation 2:

100 degrees C - 0.0 degrees C = m(1.20 V) + b - m(0.250 V)
100 degrees C = 1.20 Vm + b - 0.250 Vm
100 degrees C = 0.95 Vm + b

Now, solve for the slope (m):

m = (100 degrees C - b) / 0.95 V

Substitute the value of b from Equation 1 (b = 0.250 Vm) into the equation for m:

m = (100 degrees C - 0.250 Vm) / 0.95 V

Simplify the equation:

m = 100/0.95 - (0.250 Vm) / 0.95

m ≈ 105.26 - 0.263 Vm

Now, to find the y-intercept (b), substitute the value of m into Equation 1:

0.0 degrees C = m(0.250 V) + b

0 = (105.26 - 0.263 Vb)(0.250 V) + b

Simplify the equation and solve for b:

0 = 26.32 - 0.06575 Vb + b

0 = 26.32 + b - 0.06575 Vb

b = -26.32 + 0.06575 Vb

The conversion equation between Volts and temperature in Celsius is:

Temp. C = (105.26 - 0.263 V) + (-26.32 + 0.06575 V)

Simplifying the equation further:

Temp. C = 105.26 - 0.19725 V

Now, let's address your questions regarding working basic conversions with sig figs and temperature conversions.

For working with significant figures (sig figs), it is essential to understand the rules:

1. For addition and subtraction: The final result should have the same number of decimal places as the measurement with the fewest decimal places.
2. For multiplication and division: The final result should have the same number of significant figures as the measurement with the fewest significant figures.

In the case of the piece of metal's density calculations, you need to use the measurements provided to find the volume and then divide the mass by the volume. To calculate density in units g/cm³, convert all the measurements to the same unit (cm) and perform the calculations. For density in kg/dm³, convert the measurements to the same unit (dm) and again perform the calculations.

Concerning temperature conversions with significant figures, it is crucial to keep track of the given information and use it appropriately. Record the conversions accurately, and pay attention to any pre-determined significant figures or decimals in the given data.

To avoid confusion and ensure accuracy, it is helpful to double-check all calculations and conversions, as well as to communicate with your TA regarding any specific requirements or expectations they have for sig figs in your answers.