First slide

Change in internal energy

Question

The work of 146 kJ is performed in order to compress one kilomole of a gas adiabatically and in this process the temperature of the gas increases by 7°C. The gas is
$(R = 8 \cdot 3 J {mol}^{- 1} K^{- 1})$

Moderate

A

diatomic
B

triatomic
C

monoatomic
D

mixture of monoatomic and diatomic

Solution

For adibatic process, dQ = 0 i.e., dU = -dW
$∴ {nC}_{V} dT = 146 \times 10^{3} J$
If the the degrees of freedom, then
$\frac{nfR}{2} \times 7 = 146 \times 10^{3} ∴ \frac{10^{3} \times f \times 8 \cdot 3 \times 7}{2} = 146 \times 10^{3}$
Solving, we get $f = 5 \cdot 02 \approx 5$
So, the gas is diatomic,

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