The volume of a liquid is 630 m3 at 30°C and it is 650 m3 at 90°C. Find the coefficient of volume expansion of the liquid?
If V1 and V2 be the volumes of a liquid at temperatures T1°C and,
T2°C respectively, the coefficient of volume expansion is
| ∴ γ | = | (V2 – V1)/(V1 (t2 – t1)) |
| = | (650 – 630)/(630(90 – 30)) | |
| = | 20/(630 × 60) | |
| = | 5.29 × 10–4 per°C |
A metal cube of side 8 cm at 10°C is heated, when its each side becomes 8.5 cm at 810° C. Calculate the values of coefficients of linear, superficial and cubical expansion ?
Given L0 = 8 cm, Lt = 8.5 cm and t = 810 – 10 = 800° C
| ∴ α | = | (Lt – L0) / (L0 × t) |
| = | (8.5 – 8)/(8 × 800) | |
| = | 0.5/6400 | |
| = | 0.000078/° C. | |
| ∴ β | = | 2 × α |
| = | 2 × 0.000078/° C. | |
| = | 0.000156/° C. | |
| ∴ γ | = | 3 × α |
| = | 3 × 0.000078 /° C. | |
| = | 0.000234 /° C. |
When 500 ml of a liquid is heated in a flask from 10°C to 20°C, its volume expands by 2 ml. Calculate the coefficient of cubical expansion of the liquid (Neglect the expansion of flask)?
The coefficient of cubical expansion of a liquid is calculated by using the relation :
| Coefficient of cubical expansion | = | Increase in volume / (Original volume × Rise in temperature) |
| (or) γ | = | (V2 – V1)/(V1 × (T2 – T1)) |
| Here, Original volume of liquid, V1 | = | 500 ml |
| Increase in volume of liquid, V2 – V1 | = | 2 ml |
| Rise in temperature, T2 – T1 | = | 20° – 10° |
| = | 10°C | |
| Now, putting these values in the above formula, we get: | ||
| ∴ γ | = | 2/(500 × 10) |
| = | 0.0004 per °C | |
| = | 4 × 10 – 4 per °C | |
| Thus, the coefficient of cubical expansion of this liquid is 4 × 10 – 4 per °C. |
A 700 millilitre bottle was filled to the brim by a liquid medicine at 10°C. How much medicine will leak out at 40°C ? [Coefficient of cubical expansion (γ) of the medicine = 4.91 × 10 – 4 per ° C]. Neglect the expansion of bottle ?
When the liquid medicine is heated, it will expand and its volume will increase. The amount of liquid medicine leaking at 40°C will be equal to the increase in its volume on heating to 40°C. So, in this problem we have to calculate the increase in volume of the liquid medicine on heating. We know that the formula for the coefficient of cubical expansion of a liquid is :
| γ | = | (V2 – V1) / (V1 × (T2 – T1)) |
| Here, Coeff. of cubical expansion, γ | = | 4.91 × 10 – 4 per ° C |
| Original volume of medicine, V1 | = | 700 ml |
| Increase in volume of medicine, V2 – V1 | = | ? (To be calculated) |
| And, Rise in temperature, T2 – T1 | = | 40° – 10° |
| = | 30° C | |
| Now, putting these values in the above formula, we get: | ||
| ∴ 4.91 × 10 – 4 | = | (V2 – V1)/(700 × 30) |
| (V2 – V1) | = | 4.91 × 10 – 4 × 700 × 30 |
| = | 10.3 ml | |
| Thus, 10.3 ml of the liquid medicine will leak out at 40°C. |