Assetion : The temperature of a gas does not change when it undergoes on adiabatic process
Reason: During adiabatic process , heat energy is exchanged between a system and surroundings.

Options

A. If both assetion and reason are true and reaasons is the correct expanation of assetion
B. If both assetion and reason are tur but reason is not the correct explanation of assetion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason about the adiabatic process, we can follow these steps:

### Step 1: Understand the Assertion
The assertion states that "the temperature of a gas does not change when it undergoes an adiabatic process." We need to analyze if this statement is true or false.

### Step 2: Understand the Adiabatic Process
An adiabatic process is defined as a process in which no heat is exchanged between the system and its surroundings. This means that the heat transfer (dQ) is equal to zero.

### Step 3: Apply the First Law of Thermodynamics
According to the first law of thermodynamics, the change in internal energy (dU) of a system is related to the heat added to the system (dQ) and the work done by the system (dW) as follows:
\[ dQ = dU + dW \]
Since we established that dQ = 0 in an adiabatic process, we can rewrite this as:
\[ 0 = dU + dW \]
This implies:
\[ dU = -dW \]

### Step 4: Relate Internal Energy Change to Temperature
The change in internal energy (dU) for an ideal gas can be expressed as:
\[ dU = nC_v dT \]
where \( n \) is the number of moles, \( C_v \) is the molar heat capacity at constant volume, and \( dT \) is the change in temperature.

### Step 5: Analyze the Implications
From \( dU = -dW \), if work is done by or on the gas (which is typically the case in adiabatic processes), the internal energy must change, which means the temperature must also change. Therefore, the assertion that the temperature does not change is **false**.

### Step 6: Understand the Reason
The reason states that "during an adiabatic process, heat energy is exchanged between a system and surroundings." This is incorrect because, by definition, an adiabatic process involves no heat exchange (dQ = 0). Thus, the reason is also **false**.

### Conclusion
Both the assertion and the reason are false. Therefore, the correct answer to the question is that both the assertion and the reason are incorrect.

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