Question

The triple point of carbon dioxide is 216.55 K the corresponding temperature on the Celsius and Fahrenheit scale respectively is:
A. 56.45$^{\circ}$ C, -69.61$^{\circ}$ F
B. -56.45$^{\circ}$ C, 69.61$^{\circ}$ F
C. 56.45$^{\circ}$ C, 69.61$^{\circ}$ F
D. -56.45$^{\circ}$ C, -69.61$^{\circ}$ F

Answer 1

Hint: 273 Kelvin is the temperature that marks 0$^{\circ}$ C on Celsius scale. So, any temperature in Kelvin below 273 K will mark a negative value in Celsius scale. Proceed with this argument and use the conversion formula from Celsius to Fahrenheit.

Formula used:
For Kelvin to Celsius conversion:
Temperature in Celsius = Temperature in Kelvin - 273.
For Celsius and Fahrenheit conversion:
$F = \dfrac{9}{5} C +32$
C is temperature on Celsius scale and F is Fahrenheit temperature.

Complete step by step answer:
A triple point for an element or a compound, is a point in its pressure temperature graph which signifies the coexistence of three phases together solid, liquid and gaseous. We are given that 216.55 K is the triple point for Carbon dioxide i.e., it exists as solid, liquid and gas at that point simultaneously.
In Celsius, this temperature converts as:
T (in $^{\circ}$C) = 216.55 - 273
T = - 56.45$^{\circ}$ C.

Keeping this value for C in the temperature conversion formula from Celsius to Fahrenheit, we may write:
$F = \dfrac{9}{5} \times (- 56.45) +32$ .
After calculation, this gives,
F = - 69.61$^{\circ}$ F.

Therefore, temperature in Celsius and Fahrenheit are respectively - 56.45$^{\circ}$ C and - 69.61$^{\circ}$ F. Therefore the correct answer is option (D).

Note:
A guesswork that the given temperature is below 273 K, showing the Celsius temperature must be negative is not good enough to produce the correct answer itself. One might assume that positive temperature, the number is greater for Fahrenheit so must be the case for negative temperature but such assumption is highly wrong. One should always write down the formula and perform the required calculation instead of taking a naive guess.