A volume V0 = 1.20 m^3 expands volumetrically with coefficient beta = 7.1 × 10^-6 per °C. If the temperature rises by delta T = 100 °C, what is the change in volume delta V?

A volume V0 = 1.20 m^3 expands volumetrically with coefficient beta = 7.1 × 10^-6 per °C. If the temperature rises by delta T = 100 °C, what is the change in volume delta V?

• A. 0.00852 m^3
• B. 0.000852 m^3
• C. 0.0000852 m^3
• D. 0.0852 m^3

Answer: (B)

When a volume expands with temperature, the change in volume is proportional to the original volume and the temperature increase. The relation is delta V = beta × V0 × delta T, where beta is the volumetric expansion coefficient. Here, V0 = 1.20 m^3, delta T = 100 °C, and beta = 7.1 × 10^-6 per °C. Compute step by step: V0 × delta T = 1.20 × 100 = 120. Then delta V = (7.1 × 10^-6) × 120 = 8.52 × 10^-4 m^3. So the volume increases by delta V = 8.52 × 10^-4 m^3, which is 0.000852 m^3. The magnitude aligns with the given answer. The fractional change is beta × delta T = 7.1 × 10^-4, about a 0.071% increase.

When a volume expands with temperature, the change in volume is proportional to the original volume and the temperature increase. The relation is delta V = beta × V0 × delta T, where beta is the volumetric expansion coefficient.

Here, V0 = 1.20 m^3, delta T = 100 °C, and beta = 7.1 × 10^-6 per °C. Compute step by step: V0 × delta T = 1.20 × 100 = 120. Then delta V = (7.1 × 10^-6) × 120 = 8.52 × 10^-4 m^3.

So the volume increases by delta V = 8.52 × 10^-4 m^3, which is 0.000852 m^3. The magnitude aligns with the given answer. The fractional change is beta × delta T = 7.1 × 10^-4, about a 0.071% increase.