To find the value of absolute zero using the calibration data, we need to determine the constants A and B in the linear relationship P = A + BT.
Given the calibration points, we have two equations:
Equation 1: P1 = A + B * T1
Equation 2: P2 = A + B * T2
where T1 is the temperature of dry ice (-78.5°C) and P1 is the corresponding pressure (0.896 atm), and T2 is the boiling point of pentane (36.1°C) with P2 (1.433 atm) being the corresponding pressure.
We can rewrite both equations in terms of A and B.
Equation 1: A + B * (-78.5) = 0.896
Equation 2: A + B * 36.1 = 1.433
Now we have two linear equations with two unknowns. We can solve these equations simultaneously to find the values of A and B.
Solving Equation 1:
A - 78.5B = 0.896
Solving Equation 2:
A + 36.1B = 1.433
Multiplying Equation 1 by 36.1 and Equation 2 by 78.5 to eliminate A, we get:
36.1A - 2828.35B = 32.4256
78.5A + 2828.5B = 112.0705
Adding these two equations, we have:
114.6A = 144.4961
Dividing both sides by 114.6, we find:
A = 1.2617
Substituting A into Equation 1:
1.2617 - 78.5B = 0.896
Simplifying, we find:
-78.5B = -0.3657
Dividing both sides by -78.5, we get:
B = 0.00466
Now that we have the values of A and B, we can use the equation P = A + BT to find the values of pressures at different temperatures.
1. Given that the freezing point of water is 0°C, we can find the pressure at this temperature using Equation P = A + BT:
P = 1.2617 + 0.00466 * 0 = 1.2617 atm
2. Given that the boiling point of water is 100°C, we can find the pressure at this temperature using Equation P = A + BT:
P = 1.2617 + 0.00466 * 100 = 1.7277 atm
Therefore, the value of absolute zero obtained from the calibration is -273.15°C, the pressure at the freezing point of water is 1.2617 atm, and the pressure at the boiling point of water is 1.7277 atm.