kelvin (difference)
Temperature differenceexact by definition
The kelvin used as a temperature difference: the size of one step on the absolute scale, not a position on it. When a quantity is a change in temperature rather than a temperature, the offsets of the various scales cancel and only the ratio of degree sizes survives, so this converts by a pure factor of 1 with no offset. The factor is exact by definition.
Watch out: A difference in kelvin and a difference in Celsius degrees are numerically identical, which is why formulas are written in J/(kg·K) and then used with Celsius temperatures without any conversion. A difference in Fahrenheit degrees is not: it is 9/5 as large a number for the same physical change.
| 1 K | 1 C° |
About the kelvin (difference)
This is the distinction that catches more people than any other in this catalog, so it is worth being blunt about it. There are two different questions you can ask about temperature, and they convert by different rules.
How hot is it? That is a position on a scale, and each scale puts its zero somewhere different. 10 °C is 50 °F, because \(t_F = 1.8 \, t_C + 32\). The 32 is there because the two scales disagree about where zero should be. How much did it change? That is an interval, and when you subtract one temperature from another the offset appears on both sides and cancels. If a room goes from 10 °C to 20 °C, in Fahrenheit it went from 50 °F to 68 °F. The change is 10 Celsius degrees on one scale and 18 Fahrenheit degrees on the other. A rise of 10 C° is a rise of 18 F°, not 50 F°, and there is no addition of 32 anywhere in it.
Algebraically: \(\Delta t_F = 1.8 \, t_{C,2} + 32 - (1.8 \, t_{C,1} + 32) = 1.8 \, \Delta t_C\). The 32 vanishes. That is the entire content of the rule, and it is why this site keeps absolute temperature and temperature difference as two separate quantity types rather than one. A converter that applied the offset to a delta-T would turn a 10-degree rise into a 50-degree one.
Where does a delta-T actually show up? Almost everywhere in thermal engineering. The heat carried by a flow, \(Q = \dot{m} c_p \Delta T\). The heat through a wall, \(Q = UA\Delta T\). The supply-to-return spread on a hydronic loop, usually 20 F° or about 11 C° in North American design. The approach temperature on a heat exchanger. Every one of those is an interval, and every one of them converts by 1.8 or 5/9 and nothing else. The units K, C° and F° in this list mean exactly that: the size of a step, not a place on the dial.