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RMS and KE Expressions

Molar heat ca...

Question

Molar heat capacity of an ideal gas at constant volume is given by $C_{v} = 16.5 + 10^{- 2} T$ (in Joule). If 3.5 moles of this ideal gas are heated at constant volume from 300K to 400K the change in internal energy (in kJ) will be:

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Solution

In integral form, $\int d U = n \int_{T 1}^{T 2} C_{v} d T$

$Δ U = n \int_{T_{1}}^{T_{2}} (16.5 + 0.01 T) d T = n \int_{300}^{400} (16.5 + 0.01 T) d T$
After integration, $Δ U = 7000 J = 7 k J$
Hence, the correct answer is $7 k J .$

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