A 100 liter water tank is filled to the brim with water when the temperature is 5.00°C. Water has a coefficient of volume expansion of 207 × 10−6/°C. If the temperature of the water tank is increased to 60.0°C, what is the volume of water that overflows the tank (ignore the expansion of the tank)?
Question
A 100 liter water tank is filled to the brim with water when the temperature is 5.00°C. Water has a coefficient of volume expansion of 207 × 10−6/°C. If the temperature of the water tank is increased to 60.0°C, what is the volume of water that overflows the tank (ignore the expansion of the tank)?
Solution
To solve this problem, we need to use the formula for volume expansion, which is:
ΔV = βV0ΔT
where:
- ΔV is the change in volume,
- β is the coefficient of volume expansion,
- V0 is the initial volume, and
- ΔT is the change in temperature.
Given:
- β = 207 × 10−6/°C,
- V0 = 100 liters, and
- ΔT = 60.0°C - 5.0°C = 55.0°C.
Substituting these values into the formula, we get:
ΔV = (207 × 10−6/°C)(100 liters)(55.0°C) = 1.1385 liters.
So, 1.1385 liters of water will overflow the tank when the temperature is increased to 60.0°C.
Similar Questions
A glass container has an original volume of 1m3 and a final volume of 1.002 m3 when its temperature is increased. If the change in temperature is 30 degrees Celsius, what is the coefficient of volume expansion for the glass?
Initially when 1000.00 mL of water at 1O° C are poured into a glass cylinder, the height of the water column is 1000.0 mm. The water and its container are heated to 8O°C. Assuming no evaporation, what then will be the depth of the water column if the coefficient of thermal expansion for the glass is 3.6 x 10^-6 mm/mm per °C?
A brass box is in the shape of a cube. The coefficient of linear thermal expansion is 19 × 10−6/°C. If the temperature of the box is increased by 20°C, then what is the fractional change in the volume of the box?
A rectangular tank 15 cm long by 10 cm wide is ⅖ filled with water. The volume of water in the tank is 6 litres. How much more water is needed to fill the tank to the brim?Amount of water needed to fill the tank to the brim: ____ cm³
An open (to atmosphere), rigid-walled cylindrical tank contains 20 L of water at 40°C. Over a 2-hour period of time the water temperature varies from 40°C to 80°C. Ignoring water lost to evaporation, the volume in the tank will change as stated below:
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.