Final answer:
The question pertains to the concept of gas laws, specifically Gay-Lussac's law. With correct application of the law and calculation, it is found that the temperature on the beach, when the pressure of the gases in an aerosol can increases to 4.7 atm, is approximately 15.61°C.
Step-by-step explanation:
We can apply Gay-Lussac's law to solve this problem, which states that the pressure of a gas is directly proportional to its temperature if the volume and the amount of gas remain constant. With the values given in the question, we can set up the equation P1/T1 = P2/T2 where P refers to pressure, T refers to temperature (in Kelvin), and the subscripts 1 and 2 refer to the initial and final states.
Converting given temperatures to Kelvin (since the Kelvin scale is used in gas laws), the initial temperature T1 becomes 15°C + 273.15 = 288.15 K. Substituting the given and calculated values into the equation gives us 4.6/(288.15) = 4.7/T2. Solving this equation results in T2 = 4.7 * 288.15 / 4.6, which approximates to 288.76 K. Expressing this temperature in degrees Celsius gives us approximately 15.61°C.
So, the temperature on the beach is around 15.61°C.
Learn more about Gay-Lussac's law