Question

One mole of an ideal gas is first compressed isothermally at 380 K to half of its initial volume. Then 450 J of heat is added to it at constant volume. So, what is the network and total change in internal energy after 2 processes?

Answer 1

1. Isothermal compression:

$$W_1=nRT \ln{\frac{V_f}{V_i}}$$

$$W_1=(1)(8.31)(380)\ln{\frac{1}{2}}=-2190\ J$$

$$\Delta U_1=0$$

2.

$$W_2=0$$

$$\Delta U_2=Q=450\ J$$

Thus,

$$W=W_1=-2190\ J$$

$$\Delta U=\Delta U_2=450\ J$$