Question

A gas cylinder filled with argon is kept at a pressure of 177 atm and 25 degrees C. What is the gas pressure when the temperature of the cylinder and its contents are heated to 195 degrees C by exposure to fire?

Answer 1

`\boxed {\boxed {\sf 278 \ atm}}`

Step-by-step explanation:

We are asked to find the gas pressure when the temperature of a gas is changed. We will use Gay-Lussac's Law, which states the pressure of a gas is proportional to the temperature of the gas. The formula for this law is:

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

Initially, the pressure is 177 atmospheres and the temperature is 25 degrees Celsius or 298 Kelvin.

`\frac {177 \ atm}{298 \ K}=(P_2)/(T_2)`

Then, the gas cylinder is exposed to fire and the temperature is raised to 195 degrees Celsius or 468 Kelvin, but the pressure is unknown.

`\frac {177 \ atm}{298 \ K }=(P_2)/(468 \ K)`

We are solving for the new pressure, so we must isolate the variable P₂. It is being divided by 468 Kelvin. The inverse operation of division is multiplication, so we multiply both sides of the equation by 468 Kelvin.

`468 \ K *\frac {177 \ atm}{298 \ K}=(P_2)/(468 \ K)*468 \ K`

`468 \ K *\frac {177 \ atm}{298 \ K}=P_2`

The units of Kelvin cancel.

`468 \ K *\frac {177 \ atm}{298 \ K }=P_2`

`468 * 0.593959731544 \ atm = P_2`

`277.973154362 \ atm = P_2`

The pressure in the cylinder after exposure to fire is approximately 278 atmospheres.

Answer 2

278 atm

Step-by-step explanation:

We're gonna use this formula:
`(P_1)/(T_1) =(P_2)/(T_2)`

P₁ = 177 atm

T₁ = 298 (Convert Celsius to kelvins by adding 273)

P₂ = ?

T₂ = 468 (195 + 273)

We got

`(177)/(298) =(P_2)/(468)`

We can cross-multiply or multiply both sides by 468

I'm gonna go with the latter

`(468)(177)/(298) =(P_2)/(468)(468)`

`P_2 = ((468)(177))/(298)`

`P_2 = 277.973`