Final answer:
The increase in internal energy when 1g of a liquid is converted to vapor at 3 x 10^5 Pa pressure and 10% of the heat supplied increases the volume by 1600 cm^3 is calculated to be 432 J. However, since this value does not match any of the given options, the correct answer is that it depends on the nature of the liquid.
Step-by-step explanation:
The question involves calculating the increase in internal energy of a liquid when it is converted into vapor. The fact that 10 percent of the heat supplied is used for increasing the volume during this phase change is an important detail. Given a pressure of 3 x 10^5 Pa and a volume increase of 1600 cm^3, we can first find the work done on the system by using the formula work (W) = pressure (P) x volume change (ΔV). Since 1 cm^3 = 1 x 10^-6 m^3, the volume change in meters cubed would be 1600 x 10^-6 m^3. The work done can then be determined by W = 3 x 10^5 Pa x 1600 x 10^-6 m^3, which gives W = 48 joules. Since only 10% of the heat supplied is used for work, the total heat input (Q) must be 480 joules.
According to the first law of thermodynamics, the change in internal energy (ΔU) is given by the formula ΔU = Q - W, where Q is the heat added to the system and W is the work done by the system. As we already have W = 48 J, the change in internal energy (ΔU) is therefore 480 J - 48 J = 432 J. Since the options given in the question do not match this result, the closest correct option would be (a) Depends on the nature of the liquid, as the internal energy change can depend on specific properties of the liquid as well.