The final temperature in an adiabatic expansion is a.greater than the ...
**Adiabatic Expansion:**
Adiabatic expansion refers to a process in thermodynamics where a gas expands without any heat exchange with its surroundings. In other words, no heat enters or leaves the system during the expansion. This type of expansion is often seen in the compression and expansion of gases in engines or turbines.
**Effects of Adiabatic Expansion on Temperature:**
During an adiabatic expansion, the gas does work on its surroundings, causing its internal energy to decrease. As a result, the temperature of the gas decreases. The change in temperature depends on the specific heat capacity of the gas and the amount of work done.
To determine the final temperature of the gas after an adiabatic expansion, we need to consider the following factors:
1. **Specific Heat Capacity:** Different gases have different specific heat capacities, which determine how much the temperature of the gas changes for a given amount of work done. The specific heat capacity depends on the type of gas and its molecular properties.
2. **Amount of Work Done:** The work done during an adiabatic expansion depends on the pressure-volume (P-V) work. The more work done by the gas, the larger the decrease in temperature.
**Explanation:**
The final temperature in an adiabatic expansion is **less than the initial temperature**. This can be explained using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added or removed from the system minus the work done by or on the system.
In an adiabatic expansion, no heat is exchanged with the surroundings, so the heat term is zero. Therefore, the change in internal energy is solely due to the work done by the gas. Since work done is negative during expansion (gas does work on surroundings), the change in internal energy is negative as well.
According to the ideal gas law, the change in internal energy (ΔU) is related to the change in temperature (ΔT) and the specific heat capacity at constant volume (Cv) by the equation:
ΔU = Cv * ΔT
Since ΔU is negative in an adiabatic expansion, ΔT (change in temperature) must also be negative. This implies that the final temperature (Tf) is less than the initial temperature (Ti).
Therefore, the correct answer is **d. Less than the initial temperature**.
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