A glass bulb is filled with 0.6 m² of mercury at a temperature of 20 °C. The bulb and mercury are heated to 70°C. The linear coefficient of expansion of glass is 11 x 10-6/°C and the volume coefficient of expansion of mercury is 20 × 10-5/°C. Calculate the overflow of mercury.
To calculate the overflow of mercury, we need to consider the expansion of both the glass bulb and the mercury.
The change in volume of the glass bulb can be calculated using the formula:
ΔV_glass = V_glass * α_glass * ΔT
where:
ΔV_glass is the change in volume of the glass bulb
V_glass is the initial volume of the glass bulb
α_glass is the linear coefficient of expansion of glass
ΔT is the change in temperature
Given that the initial volume of the glass bulb is 0.6 m^3, the linear coefficient of expansion of glass is 11 x 10^-6/°C, and the change in temperature is 50°C (from 20°C to 70°C), we can calculate the change in volume of the glass bulb:
ΔV_glass = 0.6 * 11 x 10^-6 * 50 = 0.00033 m^3
Next, we need to calculate the change in volume of the mercury using the formula:
ΔV_mercury = V_mercury * β_mercury * ΔT
where:
ΔV_mercury is the change in volume of the mercury
V_mercury is the initial volume of the mercury
β_mercury is the volume coefficient of expansion of mercury
ΔT is the change in temperature
The initial volume of the mercury is equal to the volume of the glass bulb, which is 0.6 m^3. The volume coefficient of expansion of mercury is 20 x 10^-5/°C. Substituting these values into the formula, we get:
ΔV_mercury = 0.6 * 20 x 10^-5 * 50 = 0.0006 m^3
Since both the glass bulb and the mercury expand, the overflow of mercury is equal to the sum of the changes in volume of the glass bulb and the mercury:
Overflow = ΔV_glass + ΔV_mercury = 0.00033 + 0.0006 = 0.00093 m^3
Therefore, the overflow of mercury is 0.00093 m^3.