A substance is heated from –12.0oF to 150.0oF. What is its change in temperature on (a) the Celsius scales,(b) the Kelvin scales
(a) +162 F = 90 C
(b) 90 K
Each 1.8 degree rise in deg F is a 1.0 degree rise in the C or Kelvin Temperature.
To find the change in temperature on the Celsius and Kelvin scales, we need to convert the given temperatures from Fahrenheit to Celsius and Kelvin.
(a) Change in temperature on the Celsius scale:
1. Start with the initial temperature in Fahrenheit and convert it to Celsius using the formula: C = (F - 32) × 5/9.
For the initial temperature of -12.0°F:
C1 = (-12 - 32) × 5/9 = -24 × 5/9 = -13.33°C.
2. Next, convert the final temperature from Fahrenheit to Celsius:
For the final temperature of 150.0°F:
C2 = (150 - 32) × 5/9 = 118 × 5/9 = 65.55°C.
3. Calculate the change in temperature on the Celsius scale by subtracting the initial from the final temperature:
∆C = C2 - C1 = 65.55°C - (-13.33°C) = 78.88°C.
Therefore, the change in temperature on the Celsius scale is 78.88°C.
(b) Change in temperature on the Kelvin scale:
1. Convert the initial temperature from Fahrenheit to Kelvin using the formula: K = (F + 459.67) × 5/9.
For the initial temperature of -12.0°F:
K1 = (-12 + 459.67) × 5/9 = 447.67 × 5/9 = 248.71 K.
2. Convert the final temperature from Fahrenheit to Kelvin:
For the final temperature of 150.0°F:
K2 = (150 + 459.67) × 5/9 = 609.67 × 5/9 = 339.82 K.
3. Calculate the change in temperature on the Kelvin scale by subtracting the initial from the final temperature:
∆K = K2 - K1 = 339.82 K - 248.71 K = 91.11 K.
Therefore, the change in temperature on the Kelvin scale is 91.11 K.