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

Answer:

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?

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:

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

Answer:

The gases will be raised to a temperature of 803.4$^{o} C$.