Question

The pressure of neon changes from 786 mmHg to 1811 mmHg in an enclosed gas tank. Ifthe initial temperature 87°C what is the new temperature (in °C)? (Hint: changeTemp to solve the problem, change the temp back to °C). Show your workil

Answer 1

Step 1 - Find the relation between pressure and temperature

For a gas, as the temperature increases, the pressure also increases, if the volume is kept constant. We state this relation by saying that temperature and pressure are directly proportional to each other.

Since the pressure changing is happening in a enclosed tank, we don't need to worry about the volume, which will remain constant. Therefore, we can write the proportion of pressure and temperature mathematically as follows:

`(P_1)/(T_1)=(P_2)/(T_2)`

Step 2 - Substitute the values to find the new temperature

From the exercise, we have P1= 786 mmHg, P2= 1811 mmHg, T1= 87°C (360 K). We must find T2. Remember: the relation between pressure and temperature is only valid if the temperature is in K. Substituting these values on the equation given above:

`(786)/(360)=(1811)/(T_2)\rightarrow T_2=(1811*360)/(786)`

Working the math to obtain T2, we have:

`T_2=829.4\text{ K}`

Step 3 - Converting K back to °C

To convert the temperature T2 back to °C, we'll use the following relation:

`K=\degree C+273\rightarrow\degree C=K-273`

Substituting our Kelvin temperature for T2 (829.4 K), we obtain thus:

`\degree C=829.4-273=556.4\degree C`

The temperature is thus increased to 556.4 °C.