Question

assignment 4, 5. calculate the internal energy change and the heat when 5 moles nitrogen(n2) underwent a isometric process from 100°c to 50°c.

Explanation:

Step1: Determine the molar - specific heat at constant volume for N₂

N₂ is a diatomic gas. The molar - specific heat at constant volume for a diatomic gas is $C_{V}=\frac{5}{2}R$, where $R = 8.314\ J/(mol\cdot K)$.

Step2: Convert the temperatures to Kelvin

$T_1=100 + 273.15=373.15\ K$ and $T_2=50 + 273.15 = 323.15\ K$.

Step3: Calculate the change in internal energy $\Delta U$

The formula for the change in internal energy is $\Delta U=nC_{V}\Delta T$. Substituting $n = 5\ mol$, $C_{V}=\frac{5}{2}R=\frac{5}{2}\times8.314\ J/(mol\cdot K)$, and $\Delta T=T_2 - T_1=323.15 - 373.15=- 50\ K$ into the formula:
$\Delta U=n\times\frac{5}{2}R\times\Delta T=5\times\frac{5}{2}\times8.314\times(-50)$
$\Delta U=-5\times\frac{5}{2}\times8.314\times50=-5208.75\ J$.

Step4: Calculate the heat $Q$ for an isometric (constant - volume) process

For a constant - volume process, $Q = \Delta U$ according to the first law of thermodynamics $\Delta U=Q + W$, and for a constant - volume process $W = 0$. So $Q=-5208.75\ J$.

Answer:

The change in internal energy $\Delta U=-5208.75\ J$ and the heat $Q=-5208.75\ J$.