Question

What is the initial temperature (°C) of a system that has the pressure decreased by 10 times while the volume increased by 5 times with a final temperature of 150 K?

Answer 1

To find the initial temperature, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, assuming constant pressure. By converting the final temperature from Kelvin to Celsius and using the ratio of the volume change to the temperature change, we can find the initial temperature.

Step-by-step explanation:

To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin, assuming the pressure remains constant.

First, we convert the final temperature from 150 K to Celsius by subtracting 273.15: 150 K - 273.15 = -123.15 °C.

Next, we can use the ratio of the volume change to the temperature change to find the initial temperature. Since the volume increased by 5 times, the temperature must have increased by the same factor. Therefore, if the final temperature is -123.15 °C, the initial temperature would be:

-123.15 °C / 5 = -24.63 °C.

Answer 2

300K

Step-by-step explanation:

Given pressure of the system decreased by 10 times which means
`P_(2) =(P_(1) )/(10)`

Given the volume of the system increased by 5 times which means
`V_(2) =5* V_(1)`

Given final temperature
`T_(2)=150K`

Let the initial temperature be
`T_(1)`

We know that PV=nRT

As n and R are constant
`(PV)/(T)=constant`

`(P_(1)V_(1) )/(T_(1)) =(P_(2)V_(2))/(T_(2))`

`T_(1) =(P_1V_1)/(P_2V_2) T_(2)`

`T_(1) =2* T_(2)`

T1=300K