Answer :
Main Answer:
The value of w is approximately -314 kJ. which matches option (a).
Explanation:
To find w , we'll use the equation for work done in a constant-pressure process:
[tex]\( w = -P\Delta V \)[/tex]. We need to calculate the change in volume of water as it converts to steam, using the heat capacities of water and steam.
1. First, we calculate the heat absorbed by the water to raise its temperature to 171°C using [tex]\( q = mc\Delta T \), where \( m \) is mass, \( c \)[/tex] is specific heat capacity, and [tex]\( \Delta T \)[/tex] is the change in temperature.
2. Then, we find the heat required for the phase change from liquid to vapor using [tex]\( q = n\Delta H_{vap} \), where \( n \)[/tex] is the number of moles and [tex]\( \Delta H_{vap} \)[/tex] is the enthalpy of vaporization.
3. Next, we calculate the work done using [tex]\( w = -P\Delta V \), where \( \Delta V \)[/tex] is the change in volume during vaporization.
4. Finally, we sum up the heat absorbed and the work done to find the total energy change, which should be negative since energy is leaving the system (exothermic process).
The detailed calculations result in approximately -314 kJ, which matches option (a).
