# Heat Flow. Constant Volume  Fixing the piston keeps the volume constant.  If heat flows in then temperature remains the same. heat flows at base to.

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Heat Flow

Constant Volume  Fixing the piston keeps the volume constant.  If heat flows in then temperature remains the same. heat flows at base to change temperature hold fixed

Isochoric Process  For a constant volume process there is no work.  V = 0  V = 0 W = 0 W = 0  The internal energy change is only due to heat.  U = Q – W = Q  U = Q – W = Q P V isotherms

Specific Heat at Constant Volume  At constant volume the heat equals the change in internal energy.  A molar specific heat at constant volume relates to the change in temperature.  C V can be defined from the internal energy.

Constant Pressure  Allow the piston to move to keep the pressure constant. Same on both sides  Heat flows in and the piston can do work. heat flows at base to change temperature move to maintain pressure

Isobaric Process  For a constant pressure process the work is a simple product. W = P(V 2 – V 1 ) W = P(V 2 – V 1 )  The heat can be related to the internal energy change and volume change. Q =  U + WQ =  U + W Q =  U + P  VQ =  U + P  V P V isotherms

Specific Heat at Constant Pressure  The internal energy was related to the temperature change.  A molar specific heat at constant pressure relates to the change in temperature.  For and ideal gas, C P can be defined from C V.

Specific Heat for Gases  The ideal gas law predicts a simple relationship between the two forms of specific heat. C P = C V + RC P = C V + R R = 1.99 cal/mol-KR = 1.99 cal/mol-K  The table shows how close real gases are to ideal gas behavior. Gas C V C P (cal/mol-K) He2.984.97 Ne2.984.97 N 2 4.966.95 O 2 5.037.03 CO 2 6.808.83 H 2 O6.208.20 C 2 H 6 10.3012.35

No Heat  Completely insulate the system.  Allow the piston to move.  Heat can’t flow, but work can be done.  Equivalent process occurs when change is quick so little heat flows. completely insulate to block heat flow

Adiabatic Process  For an adiabatic process there is no heat flow.  U = Q – W = – W  U = Q – W = – W  There a relationship that can be derived for ideal gases. P V isotherms next

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