Question

The temperature of a rapidly expanding gas decreases. Explain why in terms of the first law of thermodynamics. (Hint: Consider whether the gas does work and whether heat transfer occurs rapidly into the gas through conduction.)

a) The gas does work, and heat transfer occurs rapidly.
b) The gas does work, but heat transfer is slow.
c) The gas does not do work, but heat transfer occurs rapidly.
d) The gas does not do work, and heat transfer is slow.

Answer 1

The temperature of a rapidly expanding gas decreases due to work done by the gas during adiabatic expansion, where heat transfer into the gas is slower than the rate of expansion, thereby lowering the gas's internal energy and temperature.

Step-by-step explanation:

The temperature of a rapidly expanding gas decreases because of the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. When a gas expands, it does work on its surroundings, and if this expansion happens faster than heat can be transferred into the gas through conduction, then the internal energy of the gas decreases, causing a decrease in temperature. Therefore, the correct answer to why the temperature of a rapidly expanding gas decreases is option (b) the gas does work, but heat transfer is slow.

In terms of thermodynamic processes, such a scenario is representative of an adiabatic expansion, where the gas does work and no heat is transferred to the gas, resulting in a drop in temperature. This is in contrast to isochoric (constant volume) or isobaric (constant pressure) processes, where different factors impact the internal energy and temperature of the gas.