One gram molecule of oxygen is heated at constant pressure from 0°C. What amount of heat should be imparted to the gas to double it's volume? Given cp = 0.218 cal g-1 0 C-1.
Answers
Given info : one gram molecule of oxygen is heated at constant pressure from 0° C.
To find : what amount of heat should be imparted to the had to double its volume ?
solution : one gram molecule means one mole.
so no of moles of oxygen gas , n = 1
work done , W = \int\limits^{2V}_{V}{p}\,dV
V
∫
2V
pdV = PV = nRT₀ = 1 × R T₀ = RT₀
internal energy change, ∆U = \int\limits^{2V}_{V}C_vdT
V
∫
2V
C
v
dT
= \int\limits^{2V}_V{\frac{R}{\gamma-1}}\,dT
V
∫
2V
γ−1
R
dT
we know, pdV = nRdT
so, \int\limits^{2V}_V{\frac{P}{\gamma-1}}\,dV
V
∫
2V
γ−1
P
dV
= \frac{pV}{\gamma-1}=\frac{RT_0}{\gamma-1}
γ−1
pV
=
γ−1
RT
0
now from 1st law of thermodynamics,
Q = W + ∆U
⇒Q = RT₀ + RT₀/(γ - 1)
for oxygen (diatomic molecule),
γ = 1.4
= 25/3 × 273 + 25/3 × 273/(1.4 - 1) J
= 2275 + 2275/0.4
= 2275 + 5687.5
= 7962.5 J
Therefore heat required to the gas to double its volume is 7962.5 J
sorry i don't know...