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Chapter 7: Problem 33

If the internal energy of a thermodynamic system is increased by \(300 .\) \(\mathrm{J}\) while \(75 \mathrm{J}\) of expansion work is done, how much heat was transferred and in which direction, to or from the system?

Short Answer

Expert verified
The heat transferred to the thermodynamic system is \(375 \text{ J}\) and the direction is into the system.

Step by step solution

01

First Law of Thermodynamics

First, let's recall the First Law of Thermodynamics, which states that the change in internal energy of a system (∆U) is equal to the heat (Q) added to the system minus the work (W) done by the system on its surroundings: \[\Delta U = Q - W\]
02

Plug in the given values

Now, we are given that the change in internal energy, ∆U, is 300 J, and the work done, W, is 75 J. We can plug these values into the equation to solve for the heat transfer (Q): \[\Delta U = Q - W\] \[300 \text{ J} = Q - 75 \text{ J}\]
03

Solve for the heat transfer, Q

Now, solving for Q, we get: \[Q = 300 \text{ J} + 75 \text{ J}\] \[Q = 375 \text{ J}\]
04

Determine the direction of heat transfer

Since Q is positive, this means that there was a transfer of heat energy into the system, as the system gained 375 J of energy. So, the heat transferred to the system is 375 J and the direction is into the system.

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