Heat transfer in an Isothermal process?

[digipony]

Homework Statement

I have a general concept inquiry. I was doing some thermal homework, and calculating values of Q in a given cycle. One process was isothermal, however it turned out that Q was not zero, causing me to wonder: How can there be a heat transfer in an isothermal process?

Homework Equations

The Attempt at a Solution

In an isothermal process the temperature does not change. Looking at the formula, Q=mcΔT, if there is no change in temperature, one would therefore find that Q=O. However, if you look at it from conservation of energy, (ΔU=Q-W), the ΔU is zero for an isothermal process, making Q=W, and thereby concluding that there is a heat transfer. Thus I am confused. Could someone please provide some insight into this?

 

[voko]

The energy of a given amount of gas is determined solely by its temperature. So if you add heat to it and want to keep its temperature constant, you will have to let the gas do the work equal to the amount of the added heat. That's what Q = W means.

 

[ehild]

Q=mcΔT is valid with different c-s -specific heat capacity values- in different processes. Remember, c=(1/m)Q/ΔT while an other state-parameter stays constant. For a constant-volume process, it is cv. In case of an isobaric process, it is cp , and it is greater than cv as part of the heat covers the work done by the gas during expansion, according to ΔU=Q-W. . The more isotherm is a process, the more is the part of work. c is not defined for the case ΔT=0. Or you can imagine that it is infinite.

ehild

 

[digipony]

I see what you are saying; that makes sense to me now. Thank you both for your explanations :)

 

[Nickie]

It is a common misconception that there is no heat transfer in an isothermal process. However, as you have correctly stated, according to the first law of thermodynamics, the change in internal energy (ΔU) is equal to the heat transfer (Q) minus the work done (W). In an isothermal process, the temperature remains constant, but this does not mean that there is no heat transfer. Instead, the heat transfer is balanced by an equal and opposite work done, resulting in no net change in internal energy. This is why Q is not zero in your calculations. In an isothermal process, the heat transfer is necessary to maintain the constant temperature, and it is balanced by work done in the opposite direction. This is an important concept in thermodynamics and understanding it will help you in future calculations.