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A fixed amount of an ideal gas is subjected to a 50% increase in absolute temperature and a 25% decrease in pressure. If the ratio of initial density to final density of the gas is x: 1, find the value of x.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

For an ideal gas: rho = PM/(RT), where M is molar mass (constant). So rho is proportional to P/T. New temperature T2 = 1.5 T1; new pressure P2 = 0.75 P1. Ratio: rho1/rho2 = (P1/P2)*(T2/T1) = (1/0.75)*(1.5) = (4/3)*(3/2) = 2. So x = 2.

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