Question

The gases in a hair spray can are at a temperature of 26.0 °C and a pressure of 25.0 lbs/in2. If the gases in the can reach a pressure of

90.0 Ibs/in?, the can will explode. To what temperature in Celsius must the gases be raised in order for the can to explode?

Answer 1

The gases in a hair spray can are at a temperature of 26.0 °C and a pressure of 25.0 lbs/in2.

If the pressure becomes
`90.0lbs/in^(2)`, what is the temperature of the gases?

Step-by-step explanation:

According to Gay lussac's law:

the pressure of a gas is directly proportional to its absolute temperature.

`P\alpha T`

`\frac{P{1} }{T{1} }=\frac{P{2} }{T{2} }`

Given,

`P1=25.0lbs/in^(2) \\P2=90.0lbs/in^(2) \\T1=26^(o) C=(26+273)K=299K\\T2=?`

Substitute these values in the above formula:

`\frac{P{1} }{T{1} }=\frac{P{2} }{T{2} }\\\\(25lbs/in^(2) )/(299K) }=\frac{90.0lbs/in^(2) }{T{2} }\\\\\\On simplification \\T2=1076.4K\\T2=(1076.4-273)^(o) C=803.4^(o) C`

Answer:

The gases will be raised to a temperature of 803.4
`^(o) C`.