when 1 g of gasoline is burned in an engine about 48 kj of heat is produced. how much mass is lost in the process? do you think this mass change could directly be measured?

The mass loss can be computed from the Einstein formula:

m = E/c^2

= 48*10^3/(3.0*10^8)^2
= 5.3*10^-13 kg
= 5.3*10^-10 g

In my opinion, that is too low to be measured.

According to a Wikipedia article,

"Exothermic chemical reactions in closed systems do not change mass, but become less massive once the heat of reaction is removed, though this mass change is much too small to measure with standard equipment."

. A 70-kg man and a 50-kg woman are in a 60-kg boat when its motor fails. The man dives into the water with a horizontal speed of 3m/s in order to swim ashore. If he changes his mind, can he swim back to the boat if his swimming speed is 1m/s? If not, can the woman change the boat's motion enough by diving off it at 3 m/s in the opposite direction? Could she then return to the boat herself if her swimming speed is also 1 m/s?

To determine the mass lost during the combustion of 1g of gasoline, we need to consider the energy released in the process.

First, we convert the heat produced during combustion from kilojoules (kJ) to joules (J). Since 1 kJ = 1000 J, 48 kJ is equal to 48,000 J.

Next, we use the energy-mass equivalence equation from Einstein's theory of relativity, E = mc^2, where E represents energy, m represents mass, and c represents the speed of light in a vacuum (approximately 3 x 10^8 m/s). Rearranging the equation, we get m = E / c^2.

Now, let's plug in the values:
m = 48,000 J / (3 x 10^8 m/s)^2
m = 48,000 J / 9 x 10^16 m^2/s^2

Simplifying further:
m ≈ 5.33 x 10^-10 kg

Therefore, the mass lost during the combustion of 1g of gasoline is approximately 5.33 x 10^-10 kg.

As for directly measuring this mass change, it would be extremely challenging due to the minuscule amount involved. Most weighing scales are not sensitive enough to accurately measure such a small change in mass. Additionally, the measurement precision might be affected by various factors such as air currents, temperature changes, and the presence of other substances around the combustion process. Hence, directly measuring this mass loss would be impractical.