If the temperature of an ideal gas is increased from $20 ^ { \circ } \mathrm { C } \text { to } 40 ^ { \circ } \mathrm { C }$ by what percent does the speed of the molecules increase?
A) 3%
B) 70%
C) 100%
D) 30%

Question

If the temperature of an ideal gas is increased from $20 ^ { \circ } \mathrm { C } \text { to } 40 ^ { \circ } \mathrm { C }$ by what percent does the speed of the molecules increase?
A)  3% 
B)  70% 
C)  100% 
D)  30%

Quizplus · Accepted Answer

The speed of molecules in an ideal gas is related to the temperature by the equation $v \propto \sqrt{T}$, where $v$ is the speed and $T$ is the temperature in Kelvin. Converting the given temperatures to Kelvin (293K to 313K) and calculating the ratio of the speeds before and after the temperature change gives a percentage increase of approximately 3%.

If the Temperature of an Ideal Gas Is Increased From 20