Chemistry Question

Question

Calculate the change in internal energy when 2.50 kl of energy is transferred as heat to 1.50 mol N2 at 298 K and 1 atm at constant pressure. Assume ideal gas. the molar heat capacity at constant pressure for N2 is 29.12

Answer 1

Δq = heat per unit mass transferred into the gas

h = enthalpy per unit mass of the gas

u = internal energy per unit mass of the gas

c_v = specific heat of the gas at constant volume

c_p = specific heat of the gas at constant pressure (given, but in other units)

γ = c_p/c_v = specific heat ratio of the gas (It is 1.4 for N₂, but you should look it up.)

 

Δq = Δh = c_pΔT ⇒  ΔT = Δq / c_p

 

Δu = c_vΔT = c_v(Δq / c_p) = Δq / (c_p/c_v) = Δq / γ

 

Then in terms of the given extensive quantities,

 

ΔU = ΔQ / γ = 2.50 kJ / 1.4 ≅ 1.79 kJ

 

(assuming you meant kJ instead of kl)

 

Note that you could also get c_v from

 

c_p - c_v = R/M

 

where R is the universal gas constant (look up in your book) and M is the molecular weight of the gas (nitrogen in this case).  Then from c_v and from knowing ΔT = Δq / c_p,

 

Δu = c_vΔT

 

Then 

 

ΔU = mc_vΔT

 

where m = mass of the gas = (number of moles)x(molecular weight) = (1.50)x(molecular weight of N₂)