The possibility of increase in the temperature of gas without adding heat to it happens in

Options

A. 1.Adiabatic exapansion
B. 2.isothermal expansion
C. 3.adiabatic compression
D. 4.isothermal compression

Explanation

To solve the question regarding the possibility of increasing the temperature of a gas without adding heat to it, we will analyze the different thermodynamic processes mentioned in the options.

### Step-by-Step Solution:

1. **Understanding the Question**: The question asks in which process the temperature of a gas can increase without the addition of heat.

2. **Reviewing Thermodynamic Processes**:
- **Isothermal Process**: In an isothermal process, the temperature remains constant (ΔT = 0). Therefore, it cannot lead to an increase in temperature without adding heat.
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings (dQ = 0).

3. **Applying the First Law of Thermodynamics**:
- The first law of thermodynamics states:
\[ dQ = dU + dW \]
- For an adiabatic process, since dQ = 0, we have:
\[ 0 = dU + dW \implies dU = -dW \]

4. **Analyzing Adiabatic Expansion**:
- In adiabatic expansion, the gas does work on the surroundings (dW is positive), which means:
\[ dU = -dW \implies dU < 0 \]
- Since the internal energy (U) is related to temperature (T) through the equation:
\[ dU = nC_v dT \]
where \(C_v\) is the specific heat at constant volume, a negative change in internal energy results in a decrease in temperature (ΔT < 0).

5. **Analyzing Adiabatic Compression**:
- In adiabatic compression, the volume of the gas decreases, and work is done on the gas (dW is negative):
\[ dU = -dW \implies dU > 0 \]
- This means that the internal energy increases, leading to an increase in temperature (ΔT > 0).

6. **Conclusion**:
- From the analysis, we conclude that the temperature of a gas can increase without adding heat to it during an **adiabatic compression**. Therefore, the correct answer is option 3.

### Final Answer:
The possibility of increasing the temperature of gas without adding heat to it happens in **adiabatic compression** (Option 3).