When an ideal diatomic gas undergoes adiabati | vedclass

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(C) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Taking the natural logarithm

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$-0.7 \%$

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(C) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Taking the natural logarithm on both sides: $\ln P + \gamma \ln V = 	ext{constant}$.Differentiating both sides: $\frac{dP}{P} + \gamma \frac{dV}{V} = 0$.Therefore,the fractional change in pressure is $\frac{dP}{P} = -\gamma \frac{dV}{V}$.For a diatomic gas,the adiabatic exponent $\gamma = \frac{7}{5} = 1.4$.Given the increase in volume $\frac{dV}{V} = 0.5 \% = 0.005$.Substituting the values: $\frac{dP}{P} = -1.4 	imes 0.5 \% = -0.7 \%$.Thus,the change in pressure is $-0.7 \%$.

When an ideal diatomic gas undergoes adiabatic expansion,if the increase in its volume is $0.5 \%$,then the change in the pressure of the gas is

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