Question

If the temperature of 1 mL of air at 1 atm and 0 degrees C is raised to 100 degrees C at the same pressure, the volume becomes 1.3671 mL. Calculate the value of absolute zero for a thermometer using air, assuming that the pressure-volume porduct is linear with absolute temperature even at 1 atm. Compare your result with the ice point temperature in Table 2.3. Ice point temperature = 273.15K

Answer 1

Fin d the ratio of volume difference and temperature difference

dV/ dT = (1.3671-1)/(100-1)

             = 0.3671 / 100

              = 0.003671

Now at absolute zero temp volume is zero so

dV/dT = (1.3671-0)/(100-T)

              => 0.003671 = 1.3671/(100-T)

               => 0.003671(100-T) = 1.3671

Hence T = -272.4 C

Now take

dV/dT = (1-0)/(0-T)

• 0.003671 = 1/(0-T)

T = -272.4C

Hence absolute temperature is -272.4C