Question

A certain sample of a gas has a volume of 20 L at 0°C and 1 atm. A plot of the experimental data of its volume against the Celsius temperature, at constant P, gives a straight line of slope 0.0741 L(C)^-1. From these data alone (without making use of the perfect gas law), determine the absolute zero of temperature in degrees Celsius.

Answer 1

-270 °C

Step-by-step explanation:

The equation of a straight line in which y (dependent variable) is plotted against x (independent variable) is given as y = mx + b. Where m is the slope of the graph and b is the intercept (y value when x = 0).

Given that the volume (V) is plotted against the Celsius temperature (T). It can be represented by the function:

V = mT + b

m = slope = 0.0741 L(C)^-1, b = intercept (value of volume at temperature of 0°) = 20 L

Hence:

V = 0.0741T + 20

At absolute zero, V = 0 L, therefore:

0 = 0.0741T + 20

0.0741T = -20

T = -20 / 0.0741

T = -269.9

T ≅ -270 °C