Question

One mole of a monatomic ideal gas is initially at 273 K and 1 atm. (a) What is the initial internal energy of the gas? (b) Find the work done on the gas when 500 J of heat are absorbed by the gas at constant pressure. What is the final internal energy of the gas? (c) Find the work done on the gas when 500 J of heat are absorbed by the gas at constant volume. What is the final internal energy of the gas?

Answer 1

a)

$$U_i=\frac{3}{2}nRT_1=\frac{3}{2}(1)(8.31)(273)=3400\ J$$

b)

$$W=Q-\Delta U=\frac{5}{2}nR(T_2-T_1)-\frac{3}{2}nR(T_2-T_1)=nR(T_2-T_1)$$

$$Q=\frac{5}{2}nR(T_2-T_1)$$

$$W=\frac{2}{5}Q=\frac{2}{5}500=200\ J$$

c)

$$W=0\ J$$

$$U_f=U_i+Q=3400+500=3900\ J$$