Distinguish between real and apparent cubic expansivity of a liquid.A glass bottle full of Mercury has mass 500g an being heated through 35°c,2,43g of Mercury are expelled. Calculate the mass of Mercury remaining in the bottle (cubic expansivity of Mercury) is 1.8×10-4 per k, linear expansivity of glass Is 8.0×10-6 per k
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The real cubic expansivity, also known as the absolute cubic expansivity or volume expansion coefficient, is a measure of how much a substance expands when its temperature increases. It is defined as the change in volume per unit volume per unit temperature change.
The apparent cubic expansivity is the observed change in volume per unit volume per unit temperature change, taking into account the expansion of the container or vessel that holds the substance. It includes the effect of both the substance's expansion and the expansion of the container.
To calculate the mass of Mercury remaining in the bottle, we can use the equation:
Mass remaining = Initial mass - Mass expelled
Given that the initial mass of the Mercury is 500g and 2.43g of Mercury is expelled, we can substitute these values into the equation:
Mass remaining = 500g - 2.43g
Mass remaining = 497.57g
Therefore, the mass of Mercury remaining in the bottle is 497.57g.
Now, let's calculate the change in volume of the Mercury. We know that the change in volume is proportional to the change in temperature and the original volume. The formula for calculating the change in volume is:
ΔV = V0 * β * ΔT
Where:
ΔV is the change in volume
V0 is the original volume
β is the cubic expansivity of Mercury
ΔT is the change in temperature
Given that the cubic expansivity of Mercury (β) is 1.8×10^-4 per K and the change in temperature (ΔT) is 35°C, we can convert the temperature change to Kelvin by adding 273 (since 1 K = 1°C + 273):
ΔT = 35 + 273 = 308 K
Now, let's substitute the values into the formula:
ΔV = V0 * β * ΔT
Since we don't know the original volume (V0), we cannot calculate the exact change in volume. However, we can still calculate the ratio of the change in volume of Mercury to the change in volume of the glass bottle using their respective cubic expansivity values.
Let's denote the change in volume of Mercury as ΔVMercury and the change in volume of the glass bottle as ΔVGlass. The cubic expansivity of the glass (α) is given as 8.0×10^-6 per K. The ratio can be calculated using the formula:
ΔVMercury / ΔVGlass = βMercury / αGlass
Substituting the given values:
ΔVMercury / ΔVGlass = (1.8×10^-4 per K) / (8.0×10^-6 per K)
ΔVMercury / ΔVGlass = 22.5
Therefore, the change in volume of Mercury is 22.5 times the change in volume of the glass bottle.
To distinguish between real and apparent cubic expansivity of a liquid, we first need to understand what these terms mean:
1. Real Cubic Expansivity: Real cubic expansivity refers to the actual change in volume of a liquid when its temperature is changed. It is a property of the liquid itself and is denoted by the symbol α_v.
2. Apparent Cubic Expansivity: Apparent cubic expansivity, on the other hand, takes into account the thermal expansion of not just the liquid but also the container in which it is held. It is denoted by the symbol β_v.
Now, let's calculate the mass of mercury remaining in the bottle using the given information:
1. We know that the mass of mercury expelled from the bottle is 2.43 g.
2. We also know the initial mass of the mercury in the bottle is 500 g.
3. So, the mass of mercury remaining in the bottle can be calculated as:
Remaining mass = Initial mass - Mass expelled
= 500 g - 2.43 g
= 497.57 g
Next, we can calculate the cubic expansivity of mercury using the given information:
1. The linear expansivity of glass is given as 8.0×10^-6 per K (denoted by α_L).
2. The real cubic expansivity of mercury is given as 1.8×10^-4 per K (denoted by α_v).
3. Apparent cubic expansivity (β_v) can be calculated using the formula:
β_v = α_v - α_L
Therefore, β_v = 1.8×10^-4 per K - 8.0×10^-6 per K
= 1.72×10^-4 per K
So, the mass of mercury remaining in the bottle is 497.57 g and the apparent cubic expansivity of mercury is 1.72×10^-4 per K.
Mg=500g
^(temperature) =35°C.
mHg expelled=2.43g
mHg remaining =?
Cubic expansivity of Mercury= 1.8×10-4K-1.
Linear expansivity of glass=8.0×10-6K-1
Apparent cubic expansivity = mass expelled÷ mass remaining × temperature rise.
Real cubic expansivity = apparent cubic expansivity + cubic expansivity of glass.
Apparent cubic expansivity + 3× linear expansivity of glass
Apparent cubic expansivity = real cubic expansivity - 3× linear expansivity of glass.
Apparent cubic expansivity= 1.8× 10-4 _ 3(8.0×10-6).
1.8×10-4_24×10-6
=0.00018_0.000024.
Apparent cubic expansivity=0.000156K-1
0.000156K-1=2.43÷mass remaining ×35
Mass remaining =2.43÷0.000156 ×35
Mass remaining = 445.05g