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Bulk Stress Due to a Temperature Increase. (a) Prove that,
Chapter 17, Problem 90P(choose chapter or problem)
Bulk Stress Due to a Temperature Increase. (a) Prove that, if an object under pressure has its temperature raised but is not allowed to expand, the increase in pressure is ??p? = ?B????T where the bulk modulus ?B and the average coefficient of volume expansion ?? are both assumed positive and constant. (b) What pressure is necessary to prevent a steel block from expanding when its temperature is increased from 20.0°C to 35.0°C?
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QUESTION:
Bulk Stress Due to a Temperature Increase. (a) Prove that, if an object under pressure has its temperature raised but is not allowed to expand, the increase in pressure is ??p? = ?B????T where the bulk modulus ?B and the average coefficient of volume expansion ?? are both assumed positive and constant. (b) What pressure is necessary to prevent a steel block from expanding when its temperature is increased from 20.0°C to 35.0°C?
ANSWER:Solution 90P Step 1: a) The coefficient of volume expansion, = V/V T Therefore, V = V T Bulk modulus, B = change in pressure/fractional change in volume B = - p / (V/V) B = - p / (V T)/V B = - p / (T) Rearranging the equation, - p = BT We should consider only the magnitude. Then, p = BT