Convert the temperatures in parts (a) and (b) and temperature intervals in parts (c) and (d):
(a) T = 85?F to ?R, ?C, K
(b) T = – 10?C to K, ?F, ?R
(c) ?T = 85?C to K, ?F, ?R
(d) ?T = 150?R to ?F, ?C, K
The correct answer and explanation is :
Let’s start with the conversions:
(a) Convert T = 85°F to °R, °C, K:
- To Rankine (°R):
[ T(°R) = T(°F) + 459.67 = 85 + 459.67 = \boxed{544.67\,°R} ] - To Celsius (°C):
[ T(°C) = \frac{5}{9}(T(°F) – 32) = \frac{5}{9}(85 – 32) = \frac{5}{9}(53) \approx \boxed{29.44\,°C} ] - To Kelvin (K):
[ T(K) = T(°C) + 273.15 \approx 29.44 + 273.15 = \boxed{302.59\,K} ]
(b) Convert T = –10°C to K, °F, °R:
- To Kelvin (K):
[ T(K) = T(°C) + 273.15 = -10 + 273.15 = \boxed{263.15\,K} ] - To Fahrenheit (°F):
[ T(°F) = \frac{9}{5}(T(°C)) + 32 = \frac{9}{5}(-10) + 32 = -18 + 32 = \boxed{14\,°F} ] - To Rankine (°R):
[ T(°R) = T(°F) + 459.67 = 14 + 459.67 = \boxed{473.67\,°R} ]
(c) Convert ΔT = 85°C to K, °F, °R:
Temperature intervals can be converted using only the scale factors (no offsets):
- To Kelvin (K):
[ \Delta T(K) = \Delta T(°C) = \boxed{85\,K} ] - To Fahrenheit (°F):
[ \Delta T(°F) = \frac{9}{5} \times 85 = \boxed{153\,°F} ] - To Rankine (°R):
[ \Delta T(°R) = \Delta T(°F) = \boxed{153\,°R} ]
(d) Convert ΔT = 150°R to °F, °C, K:
- To Fahrenheit (°F):
[ \Delta T(°F) = \Delta T(°R) = \boxed{150\,°F} ] - To Celsius (°C):
[ \Delta T(°C) = \frac{5}{9} \times 150 \approx \boxed{83.33\,°C} ] - To Kelvin (K):
[ \Delta T(K) = \Delta T(°C) = \boxed{83.33\,K} ]
Explanation (Approx. 300 Words):
Temperature conversions involve two types: absolute temperatures and temperature intervals. Absolute temperatures represent specific points on a scale, while intervals indicate a difference or change in temperature, not tied to any specific reference point.
For absolute temperatures, the formulas include offsets because the zero points of the scales differ. For example, Celsius and Kelvin differ by 273.15 (0°C = 273.15 K), and Fahrenheit differs from Celsius by both a scale factor and an offset.
Rankine (°R) is similar to Kelvin but based on Fahrenheit: 0 °R = 0 K. Thus, °R = °F + 459.67. Kelvin and Rankine use absolute zero as their starting point, making them absolute scales.
When converting temperature intervals, only the scale factor matters. This is because intervals (e.g., ΔT = 20°C) don’t depend on where the temperature scale starts — they just represent the “amount” of change. For example, an 85°C difference is the same as an 85 K difference, since Celsius and Kelvin have the same unit size.
The scale between °C and °F is a factor of 9/5, so a 1°C interval equals a 1.8°F interval. The same applies to °F and °R since they both use the same interval size, just shifted to start at absolute zero.
Understanding both absolute and interval conversions is crucial in science and engineering, particularly when dealing with thermodynamics, material behavior, or climate analysis, where precision across scales is essential.