Hello!
The answer is:
The new temperature will be equal to 4 K.
[tex]T_{2}=4K[/tex]
Why?
We are given the volume, the first temperature and the new volume after the gas is compressed. To calculate the new temperature after the gas was compressed, we need to use Charles's Law.
Charles's Law establishes a relationship between the volume and the temperature at a gas while its pressure is constant.
Now, to calculate the new temperature we need to assume that the pressure is kept constant, otherwise, the problem would not have a solution.
From Charle's Law, we have:
[tex]\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}[/tex]
So, we are given the following information:
[tex]V_{1}=500mL\\T_{1}=20K\\V_{2}=100mL[/tex]
Then, isolating the new temperature and substituting the given information, we have:
[tex]\frac{V_{1}}{T_{1}}=\frac{V_{2}}{T_{2}}[/tex]
[tex]T_{2}=\frac{T_{1}}{V_{1}}*V_{2} \\[/tex]
[tex]T_{2}=\frac{20.00K}{500mL}*100mL\\[/tex]
[tex]T_{2}=4K[/tex]
Hence, the new temperature will be equal to 4 K.
[tex]T_{2}=4K[/tex]
Have a nice day!
