How many percent should the absolute gas temperature be reduced when its volume

How many percent should the absolute gas temperature be reduced when its volume increases by 7 times, so that the pressure drops by 10 times.

If we assume that the mass of the gas is constant, then
P * V / T = const, where P – gas pressure, V – gas volume, T – absolute gas temperature.
From the conditions of the problem:
P1 * V1 / T1 = P2 * V2 / T2, where P2 = 0.1P1, V2 = 7V1.
Let’s calculate the change in the absolute gas temperature:
P1 * V1 / T1 = 0.1P1 * 7V1 / T2.
1 / T1 = 0.7 / T2.
T2 = 0.7 T1.
Answer: Since T2 = 0.7 T1, the absolute gas temperature must be reduced by 30%.



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