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Heat Capacity at Constant Volume

A vessel cont...

Question

A vessel contains helium, which expands at constant pressure when 15 kJ of heat is supplied to it. What will be the variation of the internal energy of the gas? (in kJ)

A

7

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B

8

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C

6

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D

9

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Solution

The correct option is D 9
Helium is monoatomic.
Hence, $γ = C_{p} / C_{v} = 5 / 3$
At constant pressure, heat supplied $= Δ Q = n C_{p} Δ T = 15 k J$
Internal energy change $= Δ U = n C_{v} Δ T = n C_{p} Δ T / γ = \frac{3}{5} \times 15 k J = 9 k J$

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