Question

An experimenter using a gas thermometer found the pressure at the triple point of water (0.01°C) to be 4.80 × 10⁴ Pa and the pressure at the boiling point (100°C) to be 6.50 × 10⁴ Pa. Assuming that the pressure varies linearly with temperature, use these two data points to find the Celsius temperature at which the gas pressure would be zero (that is, find the Celsius temperature of absolute zero). Pay attention to the number of significant figures. The triple point temperature is an exact number.

Answer 1

Answer:

$T = -282.33^o C$

Explanation:

As we know that the relation between temperature and pressure is a linear relation

so we have

$P - P_o = \frac{P_1 - P_o}{T_1 - T_o} (T - T_o)$

here we know that

$P_1 = 6.50 \times 10^4$

$P_o = 4.80 \times 10^4$

$T_1 = 100^o C$

$T_o = 0.01^o C$

now we will have

$P - 4.80 \times 10^4 = \frac{(6.50 - 4.80)\times 10^4}{100 - 0.01}(T - 0.01)$

$P = 4.80 \times 10^4 + 170.02(T - 0.01)$

now if P = 0

then we will have

$0 = 4.80 \times 10^4 + 170.02(T - 0.01)$

$T = -282.33^o C$