The temperature of 3 . 00 mol of an ideal diatomic gas is increased by 40 . 0 ° C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change

Question

The temperature of 3 . 00 mol of an ideal diatomic gas is increased by 40 . 0 ° C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is x 10 . Then the value of x (round off to the nearest integer) is _ _ _ _ _ _ _ _ _ . ( Given R = 8 . 31 J mol - 1 K - 1

TestHub · Accepted Answer

First, recall the formula of change in internal energy in terms of molar specific heat at constant volume and change in temperature, $∆ U = n C_{V} Δ T$ , for diatomic gas, $C_{V} = \frac{f}{2} R = \frac{5}{2} R$ , $\Rightarrow ∆ U = n \times \frac{5}{2} \times R Δ T$

$\Rightarrow \frac{Δ U}{W} = \frac{\frac{5}{2} n R Δ T}{n R Δ T} = \frac{5}{2} = \frac{25}{10}$

So, $x = 25$

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