Chapter 19: Q51P (page 580)

When $1.0 m o l$ of oxygen ( $O_{2}$ ) gas is heated at constant pressure starting at, $0 ° C$ how much energy must be added to the gas as heat to double its volume? (The molecules rotate but do not oscillate.)

Short Answer

Expert verified

Step by step solution

Given data

Number of moles of gas is $n = 1.0$

Temperature;

$\begin{matrix} T_{i} = 0 ° C \\ = 273 K \end{matrix}$

Understanding the concept

The expression for the amount of energy transferred to the gas is given by,

$Q = n C_{P} Δ T$

Here Q is the amount of energy transferred to gas, n is the number of moles, $C_{P}$ is the specific heat capacity at constant pressure and $Δ T$ is the temperature difference.

Calculate the amount of energy that must be added to the gas as heat to double its volume

The equation;

$Q = n C_{P} Δ T$

But, for diatomic gas $, C_{P} = \frac{7}{2} R$

Substitute $\frac{7}{2} R$ for $C_{P}$

$Q = \frac{7}{2} n R Δ T$ ....... (i)

At constant pressure, Boyle’s law gives,

$T \propto V ∴ \frac{T_{f}}{T_{i}} = \frac{V_{f}}{V_{i}} T_{f} = 2 T_{i} \begin{matrix} Δ T = T_{f} - T_{i} \\ = 2 T_{i} - T_{i} \\ = T_{i} \end{matrix}$

Substitute $1 m o l$ for n, $8.3145 J / m o l \cdot K$ for R and $273 K$ for $Δ T$ into the equation (i)

$\begin{matrix} Q = \frac{7}{2} (1) (8.3145) (273) \\ = 7.945 \times 10^{3} J \\ \approx 8.0 \times 10^{3} J \end{matrix}$

Therefore, the amount of energy that must be added to the gas as heat to double its volume is $8.0 \times 10^{3} J .$

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When $1.0 m o l$ of oxygen ( $O_{2}$ ) gas is heated at constant pressure starting at, $0 ° C$ how much energy must be added to the gas as heat to double its volume? (The molecules rotate but do not oscillate.)

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate the amount of energy that must be added to the gas as heat to double its volume

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When1.0 molof oxygen (O2) gas is heated at constant pressure starting at,0°C how much energy must be added to the gas as heat to double its volume? (The molecules rotate but do not oscillate.)

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate the amount of energy that must be added to the gas as heat to double its volume

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Astrophysics

Magnetism

Classical Mechanics

Geometrical and Physical Optics

Radiation

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

When $1.0 m o l$ of oxygen ( $O_{2}$ ) gas is heated at constant pressure starting at, $0 ° C$ how much energy must be added to the gas as heat to double its volume? (The molecules rotate but do not oscillate.)