# Chapter 16 - A Macroscopic Description of Matter - Conceptual Questions - Page 463: 9

(a) The pressure increases by a factor of 1.5 (b) The pressure increases by a factor of 6

#### Work Step by Step

We can use the ideal gas law to solve this question. $PV = nRT$ $P = \frac{nRT}{V}$ (a) $P_1 = \frac{nRT_1}{V_1}$ We can find an expression for the new pressure $P_2$: $P_2 = \frac{nRT_2}{V_2}$ $P_2 = \frac{nR(3T_1)}{2V_1}$ $P_2 = \frac{3}{2}~\frac{nRT_1}{V_1}$ $P_2 = 1.5~P_1$ The pressure increases by a factor of 1.5. (b) $P_1 = \frac{nRT_1}{V_1}$ We can find an expression for the new pressure $P_2$: $P_2 = \frac{nRT_2}{V_2}$ $P_2 = \frac{nR(3T_1)}{(V_1/2)}$ $P_2 = 6~\frac{nRT_1}{V_1}$ $P_2 = 6~P_1$ The pressure increases by a factor of 6.

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