Question

A metal tank with a capacity of 1700 L is completely filled with ethanol when both the tank and the ethanol are at temperature 19.0°C. Then, the tank and its contents are brought underground, where the temperature is 10.0°C. What volume of air will there be above the ethanol in the tank after the system has cooled off to the ground temperature? The coefficient of volume expansion for ethanol is Be 1.10 × 103 K 1. The tank is made of a metal for which the coefficient of linear expansion is at = 1.20 × 10-5 K-1

What volume of air Vair will there be above the ethanol in the tank after the system has cooled off to the ground temperature?

Answer 1

To find the volume of air above the ethanol in the tank after it has cooled off, we need to consider the thermal expansion of both the tank and the ethanol.

Step-by-step explanation:

To find the volume of air above the ethanol in the tank after it has cooled off to the ground temperature, we need to consider the thermal expansion of both the tank and the ethanol. The change in volume of the tank can be calculated using the equation:

ΔVtank = βtank * Vtank * ΔT

where ΔVtank is the change in volume of the tank, βtank is the coefficient of linear expansion for the tank material, Vtank is the initial volume of the tank, and ΔT is the change in temperature.

The change in volume of the ethanol can be calculated using the equation:

ΔVethanol = βethanol * Vethanol * ΔT

where ΔVethanol is the change in volume of the ethanol, βethanol is the coefficient of volume expansion for ethanol, Vethanol is the initial volume of the ethanol, and ΔT is the change in temperature.

The volume of air above the ethanol in the tank can be calculated by subtracting the change in volume of the ethanol from the change in volume of the tank:

Vair = ΔVtank - ΔVethanol

Plugging in the given values, we can find the volume of air above the ethanol in the tank after it has cooled off to the ground temperature.