Question

The temperature of a smelting furnace is found to be 2000 ℃. Find the

equivalent temperature on (a) the Fahrenheit scale (b) the Rankine

scale (c) the absolute scale (d) Reaumer scale.​

Answer 1

a) The equivalent temperature of 2000 ºC is 3632 ºF.

b) The equivalent temperature of 2000 ºC is 4091.67 R.

c) The equivalent temperature of 2000 ºC is 2273.15 K.

d) The equivalent temperature of 2000 ºC is 1600 ºRe.

Step-by-step explanation:

a) The equivalent temperature on the Fahrenheit scale is defined by the following formula:

`T_(F) = (9)/(5)\cdot T_(C)+32` (Eq. 1)

Where:

`T_(C)` - Temperature, measured in degrees Celsius.

`T_(F)` - Temperature, measured in degrees Fahrenheit.

If we know that
`T_(C) = 2000\,^(\circ)C`, then the temperature is:

`T_(F) = (9)/(5)\cdot (2000\,^(\circ)C)+32\,^(\circ)F`

`T_(F) = 3632\,^(\circ)F`

The equivalent temperature of 2000 ºC is 3632 ºF.

b) From result in a) we determine the equivalent temperature on the Rankine scale by using the following formula:

`T_(R) = T_(F)+459.67` (Eq. 2)

Where:

`T_(F)` - Temperature, measured in degrees Fahrenheit.

`T_(R)` - Temperature, measured in Rankine.

If we know that
`T_(F) = 3632\,^(\circ)F`, then the temperature is:

`T_(R) = 3632\,^(\circ)F+459.67\,R`

`T_(R) = 4091.67\,R`

The equivalent temperature of 2000 ºC is 4091.67 R.

c) The equivalent temperature on the absolute scale is calculated by using this expression:

`T_(K) = T_(C)+273.15` (Eq. 3)

Where:

`T_(C)` - Temperature, measured in degrees Celsius.

`T_(K)` - Temperature, measured in Kelvin.

If we know that
`T_(C) = 2000\,^(\circ)C`, then the temperature is:

`T_(K) = 2000\,^(\circ)C+273.15\,K`

`T_(K) = 2273.15\,K`

The equivalent temperature of 2000 ºC is 2273.15 K.

d) The equivalent temperature on the Réaumur scale is calculated by applying this expression:

`T_(Re) = (4)/(5)\cdot T_(C)` (Eq. 4)

Where:

`T_(C)` - Temperature, measured in degrees Celsius.

`T_(Re)` - Temperature, measured in degrees Réaumur.

If we know that
`T_(C) = 2000\,^(\circ)C`, then the temperature is:

`T_(Re) = (4)/(5)\cdot (2000\,^(\circ)C)`

`T_(Re) = 1600\,^(\circ)Re`

The equivalent temperature of 2000 ºC is 1600 ºRe.