Question
Question: At a constant pressure, what should be the percentage increase in the temperature in Kelvin for a \(...
At a constant pressure, what should be the percentage increase in the temperature in Kelvin for a 10% increase in the volume:
(A) 10%
(B) 20%
(C) 5%
(D) 50%
Solution
For solving this question, we need to use an equation involving the volume and temperature terms of a gas at initial and final steps at constant pressure. One equation that we are very familiar with is the equation proposed from Charles’s law. Charles’s law is a gas law, also called the law of volumes. It explains how gases tend to expand in volume when heated.
Complete answer:
Charles’s law states that:
“At constant pressure, the volume of a gas is directly proportional to its Kelvin temperature.”
⇒ V∝T
Where V and T are the volume and temperature (taken in Kelvin) of the gas.
Hence,
⇒V=kT
Where k is the proportionality constant.
⇒TV=k, a constant
⇒T1V1=T2V2
Where V1 and T1 are the initial volume and temperature of the gas respectively, and V2 and T2 are the final volume and temperature respectively.
In the question, we are asked to find the temperature increase in Kelvin when the volume of a gas increases by 10%.
We are given:
⇒V1=V1
⇒T1=T1
⇒V2=10%greater than V1
=V1+10%ofV1
=V1+(10010×V1)=V1+(10V1)
=1010V1+V1
=1011V1
⇒T2=?
Substituting the values in Charles’s law,
⇒T1V1=T2V2
T1V1=T2(1011V1)
T2=V11011V1×T1
⇒T2=1011T1
Since the final volume and final temperatures are V2=1011V1 and T2=1011T1 respectively and the percentage increase in volume is 10%, the temperature increase is also 10%.
Therefore, the required answer is (A) 10%.
Note:
Some other important gas laws are: Boyle’s law (describes relation between volume and pressure of a gas at constant temperature), Avogadro’s law (describes the relation between volume and number of moles of a gas at constant temperature and pressure), Gay Lussac’s law (describes relation between pressure and temperature of a gas at constant volume and mass).