Question

Not only is liquid nitrogen a cheaper coolant than liquid helium, its boiling point is higher (77 K vs. 4.2 K). How does higher temperature help lower the cost of cooling a material? Explain in terms of the rate of heat transfer being related to the temperature difference between the sample and its surroundings.

a) Higher temperature decreases heat transfer rate
b) Higher temperature increases heat transfer rate
c) Lower temperature is more cost-effective
d) Lower temperature decreases the need for cooling

Answer 1

Liquid nitrogen's higher boiling point means a smaller temperature difference with the surroundings, leading to slower heat transfer, reduced cooling needs, and therefore lower costs.

Step-by-step explanation:

The higher boiling point of liquid nitrogen at 77 K compared to liquid helium's 4.2 K helps lower the cost of cooling a material because the rate of heat transfer is related to the temperature difference between the sample and its surroundings. The smaller the temperature difference, the slower the heat transfer, meaning that less cooling fluid (such as liquid nitrogen) is needed to maintain the low temperature.

Since liquid nitrogen is higher in temperature than liquid helium, the temperature difference between the sample and the ambient temperature is less, resulting in a slower rate of heat loss and therefore reduced cooling requirements and costs.

In terms of heat transfer, a higher temperature helps lower the cost of cooling a material because it increases the rate of heat transfer. Heat transfer occurs when there is a temperature difference between the sample (the material being cooled) and its surroundings. The larger the temperature difference, the faster heat is transferred. So, higher temperature (in this case, the boiling point of liquid nitrogen at 77 K) results in a higher rate of heat transfer.