Question

Two systems have the following equations of state, where RR is the gas constant per mole. The mole numbers are N1​ = 3 and N2​ = 5. The initial temperatures are T1​ = 175 K and T2​ = 400 K. What is the temperature once equilibrium is reached (in Kelvin)?
1/t1=3/2(R*N1/U1)
1/t2=5/2(R*N2/U2)​

Answer 1

The temperature once equilibrium is reached can be found from the following ideal gas law. Initially, we have

$$n_1RT_1+n_2RT_2.$$

In the equilibrium, we have

$$(n_1+n_2)RT.$$

If pressure and volume did not change, we have

$$n_1RT_1+n_2RT_2=(n_1+n_2)RT,\\\space\\ T=\frac{n_1T_1+n_2T_2}{n_1+n_2}=316\text{ K}.$$