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A gas does 4.5 J of external work during...

A gas does 4.5 J of external work during adiabatic expansion. If its temperature falls by 2 K, then its internal energy will be

A

Increased by 4.5 J

B

Decreased by 4.5 J

C

Decreased by 2.25 J

D

Increased by 9.0 J

Text Solution

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The correct Answer is:
To solve the problem, we will use the first law of thermodynamics, which states: \[ \Delta U = Q - W \] Where: - \(\Delta U\) is the change in internal energy, - \(Q\) is the heat added to the system, - \(W\) is the work done by the system. ### Step-by-Step Solution: 1. **Identify the Process Type**: The problem states that the gas undergoes an adiabatic expansion. In an adiabatic process, there is no heat exchange with the surroundings, which means: \[ Q = 0 \] 2. **Apply the First Law of Thermodynamics**: Since \(Q = 0\), the first law simplifies to: \[ \Delta U = 0 - W \] This can be rewritten as: \[ \Delta U = -W \] 3. **Determine the Work Done**: The problem states that the gas does 4.5 J of external work. In thermodynamics, when work is done by the system on the surroundings, it is considered positive. Therefore: \[ W = 4.5 \, \text{J} \] 4. **Calculate the Change in Internal Energy**: Substituting the value of \(W\) into the equation for \(\Delta U\): \[ \Delta U = -4.5 \, \text{J} \] 5. **Interpret the Result**: A negative change in internal energy indicates that the internal energy of the gas has decreased. Therefore, the internal energy of the gas will decrease by 4.5 J. ### Final Answer: The internal energy will decrease by 4.5 J. ---
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