Answer
(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.
