In an Adiabatic Process (One in Which No Heat Transfer $P ^ { 5 } V ^ { 7 } = C$

question 4

Multiple Choice

In an adiabatic process (one in which no heat transfer takes place) , the pressure P and volume V of an ideal gas such as oxygen satisfy the equation $P ^ { 5 } V ^ { 7 } = C$ where $C$ is a constant. Suppose that at a certain instant of time, the volume of the gas is $2 \mathrm {~L}$ , the pressure is $100 \mathrm { kPa }$ , and the pressure is decreasing at the rate of $5 \mathrm { kPa } / \mathrm { sec }$ . Find the rate at which the volume is changing.

• A) \(14 \mathrm {~L} / \mathrm { sec }\)
• B) \(C - 14 \mathrm {~L} / \mathrm { sec }\)
• C) \(C - \frac { 1 } { 14 } \mathrm {~L} / \mathrm { sec }\)
• D) \(\frac { 1 } { 14 } \mathrm {~L} / \mathrm { sec }\)

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Definitions:

Degrees of Freedom

The number of independent values or quantities which can be assigned to a statistical distribution, minus the number of independent constraints.

Required Condition

A prerequisite or necessary condition that must be met for a certain procedure or operation to be carried out correctly.

Normally Distributed

Characterizes a probability distribution where the arrangement is mirror-imaged around the mean, suggesting that occurrences are more common near the mean than far from it.

Population Variances

A measure of the spread of a population's data points, representing the average of the squared differences from the population mean.