Question

At constant pressure, a sample of helium gas has a volume of \[800\text{ }ml\] at \[27{}^\circ C\]. Calculate the temperature at which the volume will become \[20%\] of its initial volume.
A. $20K$
B. $60{}^\circ C$
C. $150K$
D. $-213{}^\circ C$

Answer 1

Hint:-first we will take the constant values present in both the system, then equate those values in terms of volume and temperature in order to get the unknown temperature.

Complete step by step answer:
Let us write all the information we get from the question,
The volume is \[800\text{ }ml\] and temperature is \[27{}^\circ C\]
In order to convert the unit of temperature into kelvin, we will add $273$ to the given temperature.
So the temperature becomes $27+273=300K$
$20%$ of initial volume is, $0.2\times 800=160ml$
We know that,
$PV=nRT$
Where, $P$ is the pressure exerted by the gas, $V$ is the volume of gas under observation, $n$ symbolises the number of moles of that gas, $R$ is the gas constant and $T$ denotes the temperature in which the system is present.
Since pressure is also constant, we keep all the constant values and we get,
$\dfrac{V}{T}=\dfrac{nR}{P}$
So we take the ratio of initial and final volumes and the temperature which is given in the following question in order to get the unknown temperature,
\[\dfrac{V}{V_1}\times T_1=T\]
Here, the values are as followed
 $V=800ml$
$V_1=160ml$
$T_1=300K$
Now putting all the values we get, $T=60K$
Since there is no option matching our answer, we should convert the temperature into Celsius and see if it matches any option.
$60-273=-213{}^\circ C$
So the answer matches option D, hence the correct answer is D.

Note:
People usually make mistakes by forgetting to put the units. Units are an important component in questions like these as incorrect or no unit could change the answer, which will nullify all the calculations you’ve done in the whole answer.