Solids Elasticity (Bulk Modulus)

In summary, when the water freezes, it expands by about 9.00%. Using the bulk modulus of ice, the pressure increase inside an automobile engine block would be approximately 0.09 times the bulk modulus. However, if solving the problem in reverse, the pressure increase would be 0.0826 times the bulk modulus. These two answers are not equivalent as 90% of 110% of a value is not the same as the value itself.
  • #1
asoz
3
0

Homework Statement


When the water freezes it expands by about 9.00%. What pressure increase would occur inside your automobile engine block if the water in it froze?(The bulk modulus of ice is 2.00 x 10^9 N/m^2).

Homework Equations


[tex]B=\frac{\Delta P}{\Delta V / V_i}[/tex]

The Attempt at a Solution


If I solve the problem "forward in time" I get this:
[tex]\Delta P=\frac{1.09V_i-Vi}{Vi}B=0.09B[/tex]

but if solving the problem "backwards in time"

[tex] \Delta P = \frac{V_i-1.09V_i}{1.09V_i}B = 0.0826B [/tex]

Shouldn't both answers have the same magnitude?
 
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  • #2
No; 90% of 110% of x is not x, for example.
 
  • #3
Of Course. Thanks
 

Related to Solids Elasticity (Bulk Modulus)

1. What is the definition of bulk modulus?

Bulk modulus is a measure of a solid's resistance to compression under uniform pressure. It is defined as the ratio of the applied pressure to the resulting fractional decrease in volume.

2. How is bulk modulus different from Young's modulus?

Bulk modulus measures a solid's resistance to compression, while Young's modulus measures a solid's resistance to deformation in a specific direction. Bulk modulus is a more general measure of elasticity compared to Young's modulus.

3. What factors affect the bulk modulus of a material?

The bulk modulus of a material is affected by its inherent stiffness, density, and intermolecular forces. It also depends on the external conditions, such as temperature and pressure.

4. How is bulk modulus measured in experiments?

Bulk modulus is typically measured by subjecting a sample of the material to a known pressure and measuring the resulting change in volume. This can be done using various techniques, such as compression tests or ultrasonic measurements.

5. What are some practical applications of bulk modulus?

Bulk modulus is an important property in materials engineering and is used to design and test materials for various applications. It is particularly relevant in the design of structures and equipment that need to withstand high pressures, such as hydraulic systems, pressure vessels, and diving equipment. It is also used in the study of earthquake-resistant buildings and materials used in oil drilling operations.

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