A gas is placed next to a reservoir of lower temperature. The gas thus transfer 4300j of energy to the reservoir. Meanwhile, 290j of work are done on the system. By how much does the internal energy of the gas change ?
The change in internal energy of the gas can be calculated using the first law of thermodynamics:
ΔU = Q - W
where:
ΔU is the change in internal energy,
Q is the heat transferred to the gas from the reservoir (4300 J), and
W is the work done on the system (-290 J).
Substituting the given values, we have:
ΔU = 4300 J - (-290 J)
ΔU = 4300 J + 290 J
ΔU = 4590 J
Therefore, the internal energy of the gas changes by 4590 J.
To determine the change in internal energy of the gas, we can use the First Law of Thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat transferred to the system (Q) minus the work done by the system (W):
ΔU = Q - W
Given that the gas transfers 4300 J of energy to the reservoir (Q = 4300 J) and 290 J of work are done on the system (W = -290 J, where the negative sign indicates work done on the system), we can substitute these values into the equation:
ΔU = 4300 J - (-290 J)
ΔU = 4300 J + 290 J
ΔU = 4590 J
Therefore, the internal energy of the gas changes by 4590 J.