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Adiabatic process-how is internal energy mcv(t2-t1)

• Context: Graduate
• Thread starter Thread starter sreeram
• Start date Start date Nov 14, 2009
• Tags Tags Adiabatic Energy Internal Internal energy

Click For Summary

Discussion Overview

The discussion revolves around the internal energy change in an adiabatic process for an ideal gas, specifically questioning why the change is expressed as mC_V(T2-T1) rather than mC_P(T2-T1). Participants explore the implications of specific heat capacities and the nature of ideal gases.

Discussion Character

• Technical explanation
• Conceptual clarification
• Debate/contested

Main Points Raised

• Some participants propose that in a polytropic process, the internal energy change is given by mC_V(T2-T1) because it reflects the heat required at constant volume.
• Others argue that for ideal gases, the internal energy change \(\Delta U\) depends only on temperature, leading to the expression \(\Delta U=mC_V\Delta T\) being valid for any process.
• A participant questions how the relation mC_V(T2-T1) applies in an adiabatic process, noting that it is not a constant volume process.
• Another participant clarifies that the constants C_V and C_P do not imply constraints on the process type, as they can be applied broadly to ideal gases.
• There is a discussion about the assumptions underlying the behavior of ideal gases, particularly the lack of interaction between molecules, which leads to energy dependence solely on temperature.
• A later reply introduces a mathematical perspective, suggesting that starting from thermodynamic relations, one can derive that internal energy is a function of temperature under certain conditions.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of specific heat capacities in the context of adiabatic processes, with no consensus reached on the implications of these relationships.

Contextual Notes

Some limitations include the assumptions made about ideal gases, the dependence on specific heat definitions, and the conditions under which the derived relations hold. The discussion does not resolve these complexities.

sreeram Messages 10 Reaction score 0 In polytropic process internal energy change is=mCv(T2-T1)? why is it not mCp(T2-T1)? Why are we not taking specific heat at constant pressure? Last edited: Nov 15, 2009 Science news on Phys.org

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Mapes Science Advisor Homework Helper Gold Member Messages 2,591 Reaction score 21 Are you dealing with an ideal gas? If so, the internal energy is U=mC_VT+U_0=m(C_P-R)T+U_0 (the internal energy depends only on temperature), so \Delta U=mC_V\Delta T=m(C_P-R)\Delta T. C_V (or C_P-R) are just constants here. The equations apply to any process. sreeram Messages 10 Reaction score 0 mCv(t2-t1) is the heat required to raise the temperature of mass 'm' from t1 to t2 at constant volume. But adiabatic process is not a constant volume process. My question is how does this equation give the value of change in internal energy? Mapes Science Advisor Homework Helper Gold Member Messages 2,591 Reaction score 21 Are you dealing with an ideal gas? sreeram Messages 10 Reaction score 0 yes. I am dealing with ideal gas Mapes Science Advisor Homework Helper Gold Member Messages 2,591 Reaction score 21 It's a unique property of ideal gases that \Delta U=mC_V\Delta T holds for any process. The constant-volume constraint is not required. That's why I also wrote the equation as \Delta U=m(C_P-R)\Delta T, which similarly doesn't mean that constant pressure is required just because the constant-pressure specific heat appears. Again, C_V and C_P are just acting as constants, and do not represent constraints on the equation. It's hard for every thermo student to get used to this, but that's how it is. sreeram Messages 10 Reaction score 0 Thanks for the answer. But how did they found this relation? Mapes Science Advisor Homework Helper Gold Member Messages 2,591 Reaction score 21 It comes from one of the assumptions we make for an ideal gas, that there's no interaction between the atoms or molecules. If this is true, then changing the pressure (while keeping temperature constant) shouldn't have any effect on the total energy (i.e., (\partial U/\partial P)_T=0). We're left with a energy dependence on temperature alone. Gerenuk Messages 1,027 Reaction score 5 Starting from <br /> \mathrm{d}U=T\mathrm{d}S-p\mathrm{d}V<br /> one can in fact show that for the special case <br /> p=Tf(V)<br /> i.e. pressure proportional to temperature at constant volume, the energy is a function of temperature only U=A(T). The proportionality to temperature doesn't follow from it yet, but if you also assume that the density of states (statmech treatment) is a power law, the you can show that U=CT.

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