Question

The difference between $C_{p}$ and $C_{v}$ can be derived using the empirical relation H = U + pV. Calculate the difference between $C_{p}$ and $C_{v}$ for 10 moles of an ideal gas.

Answer 1

${ C }_{ p } and { C }_{ v }$ are two specific heat values at constant pressure and temperature respectively. While "solids" and "liquids" are having "only single value" for "specific heat".

${ C }_{ v }$ = "Heat capacity" at "constant volume"

${ C }_{ p }$= "Heat capacity" at "constant pressure"

The difference between ${ C }_{ p } and { C }_{ v }$ is equal to gas constant

${ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad nR$

Here,  

n = number of moles

From the given,

${ C }_{ p } and { C }_{ v } difference = 10$

${ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad 10\quad \times \quad 8.314$

${ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad 83.14\quad J$"

Answer 2

{ C }_{ p } and { C }_{ v }C

p

andC

v

are two specific heat values at constant pressure and temperature respectively. While "solids" and "liquids" are having "only single value" for "specific heat".

{ C }_{ v }C

v

= "Heat capacity" at "constant volume"

{ C }_{ p }C

p

= "Heat capacity" at "constant pressure"

The difference between { C }_{ p } and { C }_{ v }C

p

andC

v

is equal to gas constant

{ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad nRC

p

−C

v

=nR

Here,

n = number of moles

From the given,

{ C }_{ p } and { C }_{ v } difference = 10C

p

andC

v

difference=10

{ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad 10\quad \times \quad 8.314C

p

−C

v

=10×8.314

{ C }_{ p }\quad -\quad { C }_{ v }\quad =\quad 83.14\quad JC

p

−C

v

=83.14J "