Which of the following is correct expression for 1st law of thermodynamics under adiabatic condition?

Options

A. `Delta U = Q + W`
B. `Delta U = Q -W`
C. `Q = -W`
D. `Delta U = W`

Answer

To solve the question regarding the correct expression for the first law of thermodynamics under adiabatic conditions, we can follow these steps:

### Step 1: Understand the First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W). This can be expressed mathematically as:
\[ ΔU = Q + W \]

### Step 2: Define Adiabatic Conditions
In an adiabatic process, there is no heat exchange between the system and its surroundings. This means that:
\[ Q = 0 \]

### Step 3: Substitute Q in the First Law Equation
Since we know that Q is zero in an adiabatic process, we can substitute this into the first law equation:
\[ ΔU = 0 + W \]
This simplifies to:
\[ ΔU = W \]

### Step 4: Determine the Sign of Work Done
In thermodynamics, the sign of work (W) depends on the direction of energy transfer. If work is done by the system, it is considered negative (W < 0), and if work is done on the system, it is considered positive (W > 0). However, for the purpose of this question, we focus on the expression itself, which remains:
\[ ΔU = W \]

### Conclusion
Thus, the correct expression for the first law of thermodynamics under adiabatic conditions is:
\[ ΔU = W \]