Question

During a heating process, the temperature of an object rises by \(10^{\circ} \mathrm{C}\). This temperature rise is equivalent to a temperature rise of \((a) 10^{\circ} \mathrm{F}\) \((b) 42^{\circ} \mathrm{F}\) \((c) 18 \mathrm{K}\) \((d) 18 \mathrm{R}\) \((e) 283 \mathrm{K}\)

Short answer

a) 10°F b) 42°F c) 18K d) 18R e) 283K Solution: A temperature rise of 10°C is equivalent to a temperature rise of: c) 18K d) 18R

Step-by-step solution

Convert the temperature rise from Celsius to Fahrenheit

Recall that the temperature conversion from Celsius to Fahrenheit is given by the formula: \(F = \frac{9}{5} \times C + 32\). However, since we are dealing with a temperature rise, not a specific temperature, we will only use the scaling factor, as the "+32" term is an offset term. Therefore, to convert a temperature rise in Celsius to Fahrenheit, we will just use the scaling factor: \(\Delta F = \frac{9}{5} \times \Delta C\) Here, we are given a temperature rise of 10°C. So, we can calculate the equivalent temperature rise in Fahrenheit: \(\Delta F = \frac{9}{5} \times 10 = 18°F\)

Convert the temperature rise from Celsius to Kelvin

Converting a temperature rise in Celsius to Kelvin is quite simple, as the two units have the same scaling factor and only have a different offset. A temperature rise of 1°C is equivalent to a temperature rise of 1K. Thus, for a given temperature rise in Celsius, the equivalent temperature rise in Kelvin will be the same. In this case, the temperature rise of 10°C is equivalent to: \(\Delta K = 10 K\)

Convert the temperature rise from Celsius to Rankine

The Rankine scale is similar to the Fahrenheit scale; the only difference is that the Rankine scale starts at absolute zero, like the Kelvin scale. Therefore, we can convert a temperature rise in Celsius to Rankine using the same scaling factor as that used for converting Celsius to Fahrenheit, which is \(\frac{9}{5}\): \(\Delta R = \frac{9}{5} \times \Delta C\) For the given temperature rise of 10°C, the equivalent temperature rise in Rankine is: \(\Delta R = \frac{9}{5} \times 10 = 18R\)

Compare the computed results with the given options

Based on our calculations in Steps 1-3, we have the following equivalent temperature rises: 10°C = 18°F = 10K = 18R Now, let's compare our calculated results with the given options: a) 10°F (This is not equal to our calculated 18°F) b) 42°F (This is not equal to our calculated 18°F) c) 18K (This matches our calculated equivalent temperature rise in Kelvin) d) 18R (This matches our calculated equivalent temperature rise in Rankine) e) 283K (This is not equal to our calculated 10K) Thus, the temperature rise of 10°C is equivalent to a temperature rise of: c) 18K d) 18R