Finding Heat capacity of a monatomic ideal gas with a constant preassure. The problem only gives Volume and Pressure. How do you solve it, if that is the case?

Question

When a monatomic ideal gas expands at a constant pressure of 5.4 x 105 Pa, the volume of the gas increases by 4.6 x 10-3 m3. Determine the heat that flows. If heat flows into the gas, then the heat flow is positive. If the heat flows out of the gas, then the heat flow is negative.

Answer 1

Q = heat flow

U = internal energy

W = work done by system

 

Use the 1st law of thermodynamics.

 

Q = ΔU + W

 

For a monatomic ideal gas,

 

U = U(T) = (3/2)nRT

 

For any ideal gas,

 

PV = nRT

 

Then

 

U = (3/2)PV

 

At constant pressure,

 

ΔU = (3/2)PΔV = (3/2)(5.4 x 10⁵ Pa)(4.6 x 10^-3 m³) = 3726 J

W = PΔV = (5.4 x 10⁵ Pa)(4.6 x 10^-3 m³) = 2484 J

 

Q = ΔU + W = ΔU + PΔV = (3726 + 2484) J = 6210 J

 

If you also want the heat capacities, recall that for an ideal monatomic gas,

 

C_V = (3/2)R

C_P = C_V + R = (5/2)R

 

R is the universal gas constant, which you can look up.