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An insulated system contains 4 moles of an ideal diatomic gas at temperature \(T\). When a heat \(Q\) is supplied to the gas, 2 moles of the gas is dissociated into atoms and the temperature remained constant.Then the relation between \(Q\) and \(T\) is
(\(\mathrm{R}=\) universal gas constant.)
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(\(\mathrm{R}=\) universal gas constant.)
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Verified Answer
The correct answer is:
\(Q=R T\)
Given, number of moles of an ideal diatomic gas at the temperature, \(T=4\)
When heat \(Q\) is supplied to the gas, 2 mole of the gas is dissociated into atoms and the temperature remains constant, therefore
heat supplied = change in its internal energy i.e.,
\(Q=\Delta u=\left(u_f-u_i\right)\)
or \(Q=\) (internal energy of 4 moles of a monatomic gas + internal energy of 2 moles of diatomic gas) (internal energy of 4 moles of a diatomic gas)
\(\begin{aligned}
& =\left(4 \times \frac{3}{2} R T+2 \times \frac{5}{2} R T\right)-\left(4 \times \frac{5}{2} R T\right) \\
& =6 R T+5 R T-10 R T=R T
\end{aligned}\)
When heat \(Q\) is supplied to the gas, 2 mole of the gas is dissociated into atoms and the temperature remains constant, therefore
heat supplied = change in its internal energy i.e.,
\(Q=\Delta u=\left(u_f-u_i\right)\)
or \(Q=\) (internal energy of 4 moles of a monatomic gas + internal energy of 2 moles of diatomic gas) (internal energy of 4 moles of a diatomic gas)
\(\begin{aligned}
& =\left(4 \times \frac{3}{2} R T+2 \times \frac{5}{2} R T\right)-\left(4 \times \frac{5}{2} R T\right) \\
& =6 R T+5 R T-10 R T=R T
\end{aligned}\)
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