Calculate the internal energy change in each of the following cases:a) A system absorbs 15kJ of heat and does 5kJ of work.b) 5kJ of work is done on the system and 15kJ of heat is given out by the system.
Question
Calculate the internal energy change in each of the following cases:a) A system absorbs 15kJ of heat and does 5kJ of work.b) 5kJ of work is done on the system and 15kJ of heat is given out by the system.
Solution
a) The internal energy change (ΔU) of a system can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat absorbed by the system (Q) minus the work done by the system (W). Mathematically, this is represented as ΔU = Q - W.
In this case, the system absorbs 15kJ of heat (Q = 15kJ) and does 5kJ of work (W = 5kJ). Substituting these values into the equation gives:
ΔU = Q - W ΔU = 15kJ - 5kJ ΔU = 10kJ
So, the internal energy of the system increases by 10kJ.
b) In this case, 5kJ of work is done on the system (W = -5kJ, because work done on the system is considered negative) and 15kJ of heat is given out by the system (Q = -15kJ, because heat given out by the system is considered negative). Substituting these values into the equation gives:
ΔU = Q - W ΔU = -15kJ - (-5kJ) ΔU = -15kJ + 5kJ ΔU = -10kJ
So, the internal energy of the system decreases by 10kJ.
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