The temperature of an ideal gas increases in an:

Options

A. adiabatic expansion
B. isothermal expansion
C. adiabatic compression
D. isothermal compression

Answer

To determine in which process the temperature of an ideal gas increases, we need to analyze the different thermodynamic processes that can occur. Here’s a step-by-step solution:

### Step 1: Understand the Processes
We need to consider various thermodynamic processes such as isothermal, adiabatic, isobaric, and isochoric processes. Each of these processes has different effects on the temperature of an ideal gas.

### Step 2: Analyze Adiabatic Compression
In an adiabatic process, there is no heat exchange with the surroundings (i.e., \( \Delta Q = 0 \)). When an ideal gas is compressed adiabatically, the volume decreases. According to the first law of thermodynamics, the change in internal energy (\( \Delta U \)) is equal to the heat added to the system minus the work done by the system (\( \Delta U = Q - W \)). Since \( Q = 0 \) in an adiabatic process, we have:
\[ \Delta U = -W \]
Here, \( W \) is the work done on the gas, which is positive during compression.

### Step 3: Relate Internal Energy to Temperature
For an ideal gas, the internal energy is directly proportional to the temperature. Therefore, if the internal energy increases, the temperature must also increase. In adiabatic compression, since work is done on the gas, the internal energy increases, leading to an increase in temperature.

### Step 4: Conclusion
Thus, the temperature of an ideal gas increases during adiabatic compression. Therefore, the correct answer to the question is:

**Answer: Adiabatic Compression (Option C)**

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