Final answer:
To determine the final temperature of water heated by a gas expanding in a piston-cylinder assembly, we calculate the work done by the gas and equate this to the heat absorbed by the water, using the specific heat capacity of water and the computed energy transfer.
Step-by-step explanation:
The question concerns the transfer of energy as work done by a gas expanding in a piston-cylinder assembly, and the resulting temperature change in a body of water caused by this work. The gas does work against a constant external pressure, converting its energy into heat, which is absorbed by the water, thus increasing the water's temperature. To calculate the final temperature of the water, we must apply the first law of thermodynamics and the formula Q = mcΔT, where Q is the heat transferred, m is the mass of the water, c is the specific heat capacity, and ΔT is the change in temperature. The work done by the gas should equal the heat absorbed by the water (due to the assumption that all the heat goes into the water).
To find the final temperature, we first need to calculate the work done by the gas, W = PΔV, with P being the pressure and ΔV the change in volume. After obtaining the value of work done, we convert it to heat energy (Joules) absorbed by the water and use the specific heat capacity of water to compute the increase in temperature. The steps are as follows: convert the pressure to pascals, calculate the work done using the volume change, convert the work to heat, and then use the specific heat capacity of water to find the new temperature.