Chapter 19: Q42P (page 579)

What is the internal energy of $1.0 m o l$ of an ideal monoatomic gas at $273 K$ ?

Short Answer

Expert verified

The internal energy of $1.0 m o l$ of an ideal monoatomic gas at $273 K$ is $3.4 \times 10^{3} J$ .

Step by step solution

Given data

Temperature of ideal monoatomic gas, $T = 273 K$
Number of moles, $n = 1.0$

Understanding the concept

The molar specific heat $C_{V}$ of gas at constant volume is given as

$\begin{matrix} C_{V} = \frac{Q}{n Δ T} \\ = \frac{Δ E_{i n t}}{n Δ T} \end{matrix}$

Here Qis the energy transferred as heat to or from a sample of nmole of the gas, $Δ T$ is the resulting change in temperature of the gas, and $Δ E_{i n t}$ is the change in internal energy of the gas.

Calculate the internal energy of 1.0 molof an ideal monoatomic gas at

For an ideal monoatomic gas,

$C_{V} = \frac{3}{2} R$ ...... (1)

$C_{V} = \frac{Δ E_{i n t}}{n Δ T}$ ...... (2)

Substituting (1) in (2) and solving for internal energy, we get

$\begin{matrix} Δ E_{i n t} = n C_{V} Δ T \\ = \frac{3}{2} n R T \end{matrix}$

Here R is the gas constant; its value is $R = 8.31 J / mol.K$

Substituting all values in the above equation, we get

$\begin{matrix} Δ E_{i n t} = \frac{3}{2} (1.0 mol) (8.31 J / mol.K) (273 K) \\ = 3.4 \times 10^{3} J \end{matrix}$

Therefore the internal energy of $1.0 m o l$ of an ideal monoatomic gas at $273 K$ is. $3.4 \times 10^{3} J$

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What is the internal energy of $1.0 m o l$ of an ideal monoatomic gas at $273 K$ ?

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate the internal energy of 1.0 molof an ideal monoatomic gas at

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What is the internal energy of1.0 molof an ideal monoatomic gas at273 K?

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate the internal energy of 1.0 molof an ideal monoatomic gas at

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Thermodynamics

Electricity

Atoms and Radioactivity

Electric Charge Field and Potential

Turning Points in Physics

Study anywhere. Anytime. Across all devices.

What is the internal energy of $1.0 m o l$ of an ideal monoatomic gas at $273 K$ ?