A can of gasoline has a rectangular base with dimensions of 13.5 cm by 13 cm. If there are 3 liters of gasoline in the can, how much does the surface of the gasoline rise (in mm) in the can when the temperature is raised by 45C? The coefficient for volume expansion of gasoline is 9.5 10-4/C.
To determine how much the surface of the gasoline rises in the can, we need to calculate the change in volume of the gasoline due to the change in temperature. Here's how you can do it:
1. Calculate the initial volume of gasoline in the can:
- Convert the given volume of gasoline from liters to cm^3 (cubic centimeters):
1 liter = 1000 cm^3
So, initial volume = 3 liters * 1000 = 3000 cm^3 (Note: 1 cm^3 = 1 mL)
2. Calculate the change in volume of gasoline:
- Use the coefficient for volume expansion of gasoline:
Change in volume = Initial volume * Coefficient of expansion * Change in temperature
Change in volume = 3000 cm^3 * (9.5 * 10^-4 /°C) * 45°C
3. Convert the change in volume to the rise in surface level of the gasoline:
- The can has a rectangular base, so the area of the base is given by:
Area = Length * Width = 13.5 cm * 13 cm
- The rise in surface level can be calculated by dividing the change in volume by the base area:
Rise in surface level = Change in volume / Area
Now, let's substitute the values into the equations and calculate the rise in surface level:
Initial volume = 3000 cm^3
Coefficient of expansion = 9.5 * 10^-4 /°C
Change in temperature = 45°C
Area = 13.5 cm * 13 cm
Change in volume = 3000 cm^3 * (9.5 * 10^-4 /°C) * 45°C
Area = 13.5 cm * 13 cm
Rise in surface level = Change in volume / Area
Once you substitute these values and perform the calculations, you will find the rise in surface level of the gasoline in mm.
change in volume = surface area * delta h
delta volume/volume = 45 * 9.5 * 10^-4
volume = 3 liters = 3*10^-3 m*3
so
delta volume = 3 *10^-7 *45 * 9.5
= 1282*10^-7 m^3
surface area = .135*.13 = 1.755*10^-2
so
1.282*10^-4 = 1.755 *10^-2 delta h
delta h = .73 * 10^-2 meters
or .73 cm