1. A system absorbs 1.57E2 kJ of heat and the surroundings do 1.096E2 kJ of work on the system. What is the change in internal energy (in kJ) (ΔU) of the system?
2. The air in an inflated balloon (the system) absorbs 125 J of heat from its proximity to a fire. The balloon expands and does 85 kJ of work. What is the change in internal energy (in kJ) (The air in an inflated balloon (the system) absorbs 125 J of heat from its proximity to a fire. The balloon expands and does 85 kJ of work. What is the change in internal energy (in kJ) (\DeltaU) for the system? Enter only the numerical value.
1. Isn't dU = q + w? So all you need to worry about are the signs on q and w.
2. Same as 1.
1. The change in internal energy (ΔU) of the system can be calculated using the First Law of Thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat absorbed (q) minus the work done (w).
ΔU = q - w
Given:
Heat absorbed (q) = 1.57E2 kJ
Work done (w) = -1.096E2 kJ (negative sign indicates work done by the surroundings on the system)
Substituting the values:
ΔU = 1.57E2 kJ - (-1.096E2 kJ)
Simplifying:
ΔU = 1.57E2 kJ + 1.096E2 kJ
ΔU = 2.666E2 kJ
Therefore, the change in internal energy (ΔU) of the system is 2.666E2 kJ.
2. Similar to the previous question, the change in internal energy (ΔU) of the system can be calculated using the First Law of Thermodynamics:
ΔU = q - w
Given:
Heat absorbed (q) = 125 J (convert to kJ by dividing by 1000: 125 J / 1000 = 0.125 kJ)
Work done (w) = -85 kJ (negative sign indicates work done by the system)
Substituting the values:
ΔU = 0.125 kJ - (-85 kJ)
Simplifying:
ΔU = 0.125 kJ + 85 kJ
ΔU = 85.125 kJ
Therefore, the change in internal energy (ΔU) of the system is 85.125 kJ.
To determine the change in internal energy (ΔU) of a system, we can use the First Law of Thermodynamics, also known as the Law of Energy Conservation:
ΔU = Q - W
Where:
ΔU is the change in internal energy of the system
Q is the heat absorbed by the system
W is the work done on the system
Let's apply this formula to the given questions.
1. For the first question:
Q = 1.57E2 kJ (Given heat absorbed)
W = 1.096E2 kJ (Given work done on the system)
ΔU = Q - W
ΔU = 1.57E2 kJ - 1.096E2 kJ
ΔU = 47 kJ
Therefore, the change in internal energy of the system is 47 kJ.
2. For the second question:
Q = 125 J = 0.125 kJ (Given heat absorbed, converting J to kJ)
W = 85 kJ (Given work done on the system)
ΔU = Q - W
ΔU = 0.125 kJ - 85 kJ
ΔU = -84.875 kJ
Therefore, the change in internal energy of the system is -84.875 kJ. (Note: It is negative which indicates that the system lost internal energy.)
I hope this helps! Let me know if you have any other questions.