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Chapter 12: Q 60. (page 932)

The ideal gas law states that the pressure, P , volume, V, temperature in degrees Kelvin, T, and amount, n, of a gas are related by the equationP = nRT/ V, where R is the universal gas constant. In Exercises 57–60, assume that the amount of the gas is constant and evaluate the specified limits.
If the temperature is held fixed, what is $\lim_{v \to \infty} P$ ? Explain why this makes sense

Short Answer

Expert verified

The value of $\lim_{v \to \infty} P$ is $0$ .When $T$ is constant.

This makes sense because as the gas expands, the contact between the gas particles decreases rapidly, resulting in a rapid drop in pressure.

Step by step solution

01

Step 1. Given information.

We have given expression: $\lim_{v \to \infty} P$

02

Evaluate the specified limits. Explain why this makes sense

$\lim_{V \to \infty} P = \lim_{V \to \infty} \frac{n R T}{V} = n R T \lim_{v \to \infty} \frac{1}{V} = 0$

Therefore, the value of $\lim_{V \to \infty} P$ is $0$ . When T is constant.

This predicts that if a gas is allowed to expand endlessly with constant temperature, its pressure P will approach zero.

This makes sense because as the gas expands, the contact between the gas particles decreases rapidly, resulting in a rapid drop in pressure.

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