---
title: "Strength of paste: 300 gm cement"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:cement-strength-300g-150g"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/cement-strength-300g-150g
site: BCT Engineering
---

# Strength of paste: 300 gm cement

Concrete Technology and Masonry Structure · Chapter 4: Properties of hardened concrete

- Asked in: 2079 Bhadra, 6 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/cement-strength-300g-150g
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Calculate the compressive strength of cement when 300 gm of cement is mixed with 150 gm of water. Consider: Case I - cement is fully hydrated; Case II - 60% of cement is hydrated.

## Short answer

Using Powers' model with gel/space ratio x = 0.657α/(0.319α + w/c) and strength = 240x³ MPa: for full hydration (α=1, w/c=0.5) x=0.802, strength=123.9 MPa; for 60% hydration (α=0.6) x=0.570, strength=44.5 MPa.

## Answer

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.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. 300 g cement mixed with 150 g water gives w/c of:
   A. 0.5
   B. 2.0
   C. 0.45
   D. 0.2
   Answer: A. w/c = 150/300 = 0.5. (Key point: w/c ratio)

2. Gel/space ratio at full hydration, w/c 0.5, is:
   A. 0.570
   B. 0.802
   C. 0.854
   D. 0.657
   Answer: B. x = 0.657/(0.319+0.5) = 0.802. (Key point: Full hydration)

3. At 60% hydration the gel/space ratio is obtained by:
   A. 0.6 x 0.802 = 0.481
   B. 0.657/(0.319 + 0.5 x 0.6) = 0.82
   C. 0.657(0.6)/(0.319(0.6)+0.5) = 0.570
   D. 0.657(0.6)/(0.319+0.5) = 0.481
   Answer: C. Alpha multiplies both gel and cement-volume terms but not w/c. (Key point: 60% hydration)

4. Compressive strengths for Case I and Case II are:
   A. 44.5 MPa and 123.9 MPa
   B. 123.9 MPa and 44.5 MPa
   C. 149.7 MPa and 55.7 MPa
   D. 240 MPa and 144 MPa
   Answer: B. 240 x 0.802^3 = 123.9 MPa; 240 x 0.570^3 = 44.5 MPa. (Key point: Strength values)

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