Chapter 19: Q50P (page 580)

We give $70 J$ as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

Short Answer

Expert verified

Step by step solution

Given data

Heat energy given to a diatomic gas is $Q = 70 J$

Understanding the concept

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

$Q = n C_{V} Δ T$

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

Calculate by how much the internal energy of the gas increases

$Δ E_{i n t} = {nC}_{V} Δ T$

But, for diatomic gas $, C_{V} = \frac{5}{2} R$

Hence,

$Δ E_{i n t} = \frac{5}{2} n R Δ T$ …… (i)

Also, $Q = n C_{P} Δ T$

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

Hence,

$\begin{matrix} Q = \frac{7}{2} n R Δ T \\ n R Δ T = \frac{2}{7} Q \end{matrix}$

Substitute $\frac{2}{7} Q$ for $n R Δ T$ into the equation (i)

$Δ E_{i n t} = \frac{5}{2} (\frac{2}{7} Q)$

Substitute $70 J$ for Q into the above equation,

$\Rightarrow Δ E_{i n t} = 50 J$

Therefore, the increase in the internal energy is $50 J .$

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We give $70 J$ as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate by how much the internal energy of the gas increases

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We give70 Jas heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

Short Answer

Step by step solution

Given data

Understanding the concept

Calculate by how much the internal energy of the gas increases

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Geometrical and Physical Optics

Oscillations

Medical Physics

Work Energy and Power

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Study anywhere. Anytime. Across all devices.

We give $70 J$ as heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?