Question

A can of spray paint contains nitrogen gas as the propellant. The pressure of the gas is 3.5 atm when the temperature is 20.˚C. The can is left in the sun, and the temperature of the gas increases to 50.˚C. What is the pressure in the can?

Answer 1

Answer:

The new pressure is 3.86 atm

Explanation:

Step 1: Data given

The initial pressure = 3.5 atm

The temperature = 20.0 °C = 293 K

The temperature increases to 50°C = 323 K

Step 2: Calculate the new pressure

P1/T1 = P2/T2

⇒with P1 = the initial pressure = 3.5 atm

⇒with T1 = the initial temperature = 293 K

⇒with P2 = the new pressure = TO BE DETERMINED

⇒with T2 = the increased temperature = 323 K

3.5 atm/293 K = P2 / 323 K

P2 = (3.5/293) * 323

P2 = 3.86 atm

The new pressure is 3.86 atm

Answer 2

The new pressure in the can will be "3.86 atm".

Pressure and temperature:

The pressures of a specified amount of gaseous elements seem to be exactly proportional to their temperature. As such a platform's temperature rises, so does its pressure, as well as simultaneously.

According to the question,

Initial pressure, P₁ = 3.2 atm

Initial temperature, T₁ = 293 K

Increased temperature, T₂ = 323 K

Let,

The increased or new pressure be "P₂".

We know the relation,

→ $\frac{P_1}{T_1} = \frac{P_2}{T_2}$

New pressure,

P₂ = $\frac{P_1 T_2}{T_2}$

By substituting the values, we get

P₂ = $\frac{3.5\times 323}{293}$

    = $\frac{1130.5}{293}$

    = $3.86$ atm

Thus the answer above is right.    

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