At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _____ J.

We are given that the degrees of freedom per molecule of a gas is $$f = 8$$, and the gas performs $$W = 150 \text{ J}$$ of work when expanding under constant pressure. We need to find the heat absorbed.

For a gas with $$f$$ degrees of freedom, the molar heat capacity at constant volume is $$C_v = \frac{f}{2}R = \frac{8}{2}R = 4R$$, and the molar heat capacity at constant pressure is $$C_p = C_v + R = 4R + R = 5R$$.

At constant pressure, the work done by the gas is $$W = nR\Delta T$$, and the heat absorbed is $$Q = nC_p\Delta T$$.

Taking the ratio, $$\frac{Q}{W} = \frac{nC_p\Delta T}{nR\Delta T} = \frac{C_p}{R} = \frac{5R}{R} = 5$$.

So $$Q = 5W = 5 \times 150 = 750 \text{ J}$$.

Hence, the amount of heat absorbed by the gas is $$\textbf{750}$$ J.