Strength of paste: 300 gm cement

Powers' model gives the strength of concrete in terms of the gel/space ratio $x$:

$$x = \frac{\text{volume of gel}}{\text{volume of gel} + \text{capillary pores}} = \frac{0.657\,\alpha}{0.319\,\alpha + w/c}$$

where $\alpha$ is the degree of hydration and $w/c$ the water-cement ratio by mass. The numbers come from cement of specific gravity about 3.14: 1 g of cement has 0.319 cm$^3$ volume and produces gel of $2.06\times0.319 = 0.657$ cm$^3$ (including gel pores). Compressive strength:

$$f_c = 240\,x^3\ \text{MPa}$$

(240 MPa is the intrinsic strength of the gel; it varies from about 234 to 255 MPa for different cements.) The ratio $x$ does not depend on the mass of cement; the mass is only needed to give volumes.

Given

Cement = 300 g; water = 150 g; so $w/c = 150/300 = 0.5$.

Case I: fully hydrated ($\alpha = 1$)

$$\begin{aligned} x &= \frac{0.657}{0.319+0.5} = \frac{0.657}{0.819} = 0.802 \\ f_c &= 240\times0.802^3 = 123.9\ \text{MPa} \end{aligned}$$

Case II: 60% hydrated ($\alpha = 0.6$)

$$\begin{aligned} x &= \frac{0.657\times0.6}{0.319\times0.6+0.5} = \frac{0.3942}{0.6914} = 0.570 \\ f_c &= 240\times0.570^3 = 44.5\ \text{MPa} \end{aligned}$$

Answer: Case I gives gel/space ratio 0.802 and strength 123.9 MPa; Case II gives 0.570 and 44.5 MPa.