Question 1 of 20beginner🔧 ApplyNumerical2 marks

The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales.

Correct Answer

For Neon: Celsius scale: -248.58 °C Fahrenheit scale: -415.44 °F

For Carbon Dioxide: Celsius scale: -56.60 °C Fahrenheit scale: -69.88 °F

Exercise: EXERCISES | Q: 10.1 | (Page 22)
For More Understanding

Explanation

To solve this, we use the exact relation between Kelvin and Celsius scales provided in the 'Points to Ponder' section: T=tc+273.15T = t_c + 273.15. Rearranging this gives tc=T−273.15t_c = T - 273.15. For the Fahrenheit conversion, the context states there are 180 intervals on the Fahrenheit scale and 100 on the Celsius scale between the ice and steam points. This establishes the relation tF=95tc+32t_F = \frac{9}{5}t_c + 32. We apply these formulas to the given triple point temperatures.

Solution Steps

  1. Step 1: Convert Neon temperature to Celsius. Given T=24.57T = 24.57 K. Using the relation tc=T−273.15t_c = T - 273.15: tc=24.57−273.15=−248.58t_c = 24.57 - 273.15 = -248.58 °C.

  2. Step 2: Convert Neon temperature to Fahrenheit. Using the relation tF=95tc+32t_F = \frac{9}{5}t_c + 32:

    tF=95(−248.58)+32t_F = \frac{9}{5}(-248.58) + 32

    tF=−447.444+32=−415.444t_F = -447.444 + 32 = -415.444 °F. Rounding to two decimal places: -415.44 °F.

  3. Step 3: Convert Carbon Dioxide temperature to Celsius. Given T=216.55T = 216.55 K. Using the relation tc=T−273.15t_c = T - 273.15: tc=216.55−273.15=−56.60t_c = 216.55 - 273.15 = -56.60 °C.

  4. Step 4: Convert Carbon Dioxide temperature to Fahrenheit. Using the relation tF=95tc+32t_F = \frac{9}{5}t_c + 32:

    tF=95(−56.60)+32t_F = \frac{9}{5}(-56.60) + 32

    tF=−101.88+32=−69.88t_F = -101.88 + 32 = -69.88 °F.

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