The first law of thermodynamics may be expressed as shown: ∆U=Q+WWhere ∆U is the change of internal energy, Q is the heating of the system, W is the work done on the system. A fixed mass of ideal gas at high pressure is contained in a balloon. The balloon suddenly bursts, causing the gas to expand and cool. In this situation, which row describes the values of ∆U, Q and W?
Correct answer: B. ∆U is negative, Q is zero, W is negative
- A. ∆U is positive, Q is zero, W is positive
- B. ∆U is negative, Q is zero, W is negative
- C. ∆U is zero, Q is zero, W is positive
- D. ∆U is positive, Q is positive, W is zero
Explanation
When the balloon bursts, the gas undergoes rapid adiabatic expansion, meaning there is no heat exchange with the surroundings (Q = 0). According to the first law of thermodynamics, ∆U = Q + W. Here, work is done by the gas as it expands, making W negative. Consequently, the internal energy decreases (∆U is negative) as the gas cools. This makes Option B correct. Option A wrongly suggests an increase in internal energy. Option C incorrectly assumes no change in internal energy. Option D assumes a positive internal energy change and a non-zero heat exchange, both of which are incorrect in this context.
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About First Law of Thermodynamics
The first law relates heat supplied, work done and the change in internal energy through energy conservation. Problems use sign conventions and apply the law to isothermal, adiabatic, isobaric and isochoric processes. Internal energy is a state function, while heat and work depend on the path followed.
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