Section Six - Heat Capacity

what is the equation for constant volume heat capacity

CV = (d(dash)Q/dT)V

what is the equation for constant volume heat capacity as a function of T

Cv(T) = (partial d U /partial d U)V

what is the difference between CV and cV

CV is extensive and cV is intensive

why is it not ideal that CV is extensive

it would be better to have a measured quantity that is independent of how much water we used for the experiment

what is the equation to link cV and CV

cV = CV/m or cV = CV/n

what is equation relating Q and R

d(bar)Qv/dt = I²R

how do you find the equation relating Q and R

if we have boundary one being a body of water that is heated by a resistor and a second boundary being electrical work transfer to resistor. For boundary one dU = d(bar)Qv and boundary two we have dU = -d(dash)W where d(dash)W = -I²Rdt

why is constant pressure better than constant volume

heating things in a sealed rigid container is cumbersome and dangerous

what does isobaric mean

constant pressure

what is the differential first law equation for fluids at a constant pressure

dU = d(dash)Q - PdV

what is the equation for the total differential of z=f(x,y)

df = (df/dx)y dx + (df/dy)x dy

what is maxima or minima of the function

df = 0

what is the reciprocosity relation

(dx/dy)z = [(dy/dx)z]^-1

what is the cyclic relation

(dx/dy)z(dy/dz)x(dz/dx)y = -1

what is the equation for isobaric heat capacity

Cp = (d(dash)/dT)p

what is the equation for relating Cp to internal energy

Cp = Cv + [P + (dU/dV)T](dV/dT)p

how is the relation between Cp and internal energy derived

divide first law at constant pressure by dT at constant P, use the total differential equation for U = U(T,V), divide this by dT and sub into original equation

equation for specific heat capacity at constant volume for an ideal gas

cv 3/2R

what is molar specific heat capacity at constant pressure for an ideal gas

cp = cv + R

how is cp = cv + R derived

for an ideal gas U = U(T) so (dU/dV)T = 0 and (dV/dT)p = nR/P so the equation relating cP and U can be simplified

what is the ratio of the heat capacities

gamma = cp/cv

what is gamma for a monoatomic ideal gas

5/3

what is an adiabatic process

an adiabatic process is one in which there is no energy exchange by heat transfer so d(dash)Q = 0

for one mole of gas what is the constant equations for an ideal gas

TV^(gamma-1) = constant and PV^gamma= constant

how is TV^(gamma-1) = constant found

since d(dash)Q = 0, dU = -PdV and dU = cvdT so cvdT + RT/vdV = 0 which can be rewritten using cp = cv + R to be dT/T + (cp-cv/cv) dV/V = 0 which integrates to give eqn

what are isotherms

graphs of constant PV

what are adiabats

graphs of PV^gamma = constant

why are adiabats steeper than isotherms

gamma > 1

what are the slopes of isotherms and adiabats on log axes

-1 and - gamma respectively