isothermal

isobaric

isovolumetric

adiabatic

 constant property

temperature

pressure

volume

none

combined-gas law

PV graph

Work done by
the gas
area under
 PV graph

nRT [ ln (V₂ / V₁) ]

P( V₂ - V₁)

0

- DU

Q
+ if temp inc
- if temp dec

mc_VDT
nC_VDT
C_V is the molar specific heat

mc_PDT
nC_PDT
C_P is the molar specific heat

mc_VDT
nC_VDT
C_V is the molar specific heat

0

DU
+ if temp inc
- if temp dec

0

mc_VDT
nC_VDT

mc_VDT
nC_VDT

mc_VDT
nC_VDT

1st Law relationships

Q_added = W_{done by}
                   ^{the gas}

As the gas expands, the energy is supplied from the addition of heat

simplifying
C_P = C_V +nR

Q = DU

The internal energy of the gas increases as a result of the addition of heat - no work is done

0 = DU + W_{done by}
                   ^{the gas}

Any work done by the gas is at the expense of its internal energy - adiabatic expansions cause gases to get colder.

DS = Q / T

nR [ ln (V₂ / V₁) ]

nC_P [ ln (T₂ / T₁) ]

nC_V [ ln (T₂ / T₁) ]

0

isothermal

isobaric

isovolumetric

adiabatic