Chapter 3: Q20E (page 641)

When a quantity of monatomic ideal gas expands at a constant pressure of $4 \times 10^{4} P a$ , the volume of the gas increases fromrole="math" localid="1664296449974" $2 \times 10^{- 3} m^{3}$ to $8 \times 10^{- 3} m^{3}$ . What is the change in the internal energy of the gas?

Short Answer

Expert verified

The change in the internal energy would be 360J.

Step by step solution

Find a new relation of internal energy

At constant pressure, the formula for the ideal gas is $p Δ V = n R Δ T$ .

Where nrepresents the number of moles, Ris the gas constant and has the value of 8.314J/mol.K. The change in temperature is due to the change in volume.

The change in internal energy for any gas is represented by

$Δ U = n C_{V} Δ T Δ U = n (\frac{3}{2} R) Δ T \frac{2}{3} Δ U = n R Δ T$

Clearly, we can write $\frac{2}{3} ∆ U = p ∆ U$ .

Put the values and calculate the change in internal energy

Given that $p = 4 \times 10^{4} P a, V_{2} = 8 \times 10^{- 3} m^{3}$ and $V_{1} = 2 \times 10^{- 3} m^{3}$ .

$\frac{2}{3} Δ U = p Δ V Δ U = \frac{3}{2} p (V_{2} - V_{1}) Δ U = \frac{3}{2} \times 4 \times 10^{4} \times (8 \times 10^{- 3} - 2 \times 10^{- 3}) Δ U = 360 J$

So, the change in the internal energy would be 360J.

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When a quantity of monatomic ideal gas expands at a constant pressure of $4 \times 10^{4} P a$ , the volume of the gas increases fromrole="math" localid="1664296449974" $2 \times 10^{- 3} m^{3}$ to $8 \times 10^{- 3} m^{3}$ . What is the change in the internal energy of the gas?

Short Answer

Step by step solution

Find a new relation of internal energy

Put the values and calculate the change in internal energy

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When a quantity of monatomic ideal gas expands at a constant pressure of 4×104Pa, the volume of the gas increases fromrole="math" localid="1664296449974" 2×10-3m3to 8×10-3m3. What is the change in the internal energy of the gas?

Short Answer

Step by step solution

Find a new relation of internal energy

Put the values and calculate the change in internal energy

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Work Energy and Power

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Study anywhere. Anytime. Across all devices.

When a quantity of monatomic ideal gas expands at a constant pressure of $4 \times 10^{4} P a$ , the volume of the gas increases fromrole="math" localid="1664296449974" $2 \times 10^{- 3} m^{3}$ to $8 \times 10^{- 3} m^{3}$ . What is the change in the internal energy of the gas?