A sealed cylinder fitted with a movable piston contains ideal gas at $27 ^ { \circ } \mathrm { C }$ pressure $0.500 \times 10 ^ { 5 } \mathrm {~Pa}$ and volume $1.25 \mathrm {~m} ^ { 3 }$ What will be the final temperature if the gas is compressed to $0.800 \mathrm {~m} ^ { 3 }$ the pressure rises to $0.820 \times 10 ^ { 5 } \mathrm {~Pa} ?$
A) $42 ^ { \circ } \mathrm { C }$
B) $150 ^ { \circ } \mathrm { C }$
C) $250 ^ { \circ } \mathrm { C }$
D) $130 ^ { \circ } \mathrm { C }$
E) $68 ^ { \circ } \mathrm { C }$

Question

Quizplus · Accepted Answer

Using the ideal gas law, we have:$$PV = nRT$$where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.Since the number of moles of gas and the ideal gas constant are constant, we can write:$$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$$where the subscripts 1 and 2 refer to the initial and final states of the gas, respectively.Substituting the given values, we get:$$\frac{(0.500 \times 10^5 \mathrm{~Pa})(1.25 \mathrm{~m}^3)}{273 \mathrm{~K}} = \frac{(0.820 \times 10^5 \mathrm{~Pa})(0.800 \mathrm{~m}^3)}{T_2}$$Solving for T2, we get:$$T_2 = 315 \mathrm{~K} = 42 ^ { \circ } \mathrm { C }$$Therefore, the final temperature is $42 ^ { \circ } \mathrm { C }$.

A Sealed Cylinder Fitted with a Movable Piston Contains Ideal 27∘C27 ^ { \circ } \mathrm { C }27∘C

A Sealed Cylinder Fitted with a Movable Piston Contains Ideal $27 ^ { \circ } \mathrm { C }$