Question

A boiler raises the temperature of 20m³ water from 35°C to steam at 175°C. The carnot engine is 40% efficient.

b) Determine the total heat energy (in kJ) that must be supplied to the boiler to generate the steam.
c) If the heat supplied to the boiler is 60,000 KJ, determine the work output from the cycle.
d) If the pressure of steam at 175°C is reduced isothermally to 7 bars, what will be the phase?

Answer 1

To calculate the total heat energy for water to steam transformation, we use the specific heat capacity and latent heat of vaporization, and for the work output, we apply the efficiency formula of a Carnot engine. Lastly, at 175°C and 7 bars, water is in the superheated steam phase.

Step-by-step explanation:

To solve this physics thermodynamics problem, we must first calculate the total heat energy required to convert water at 35°C to steam at 175°C. To do this, we must consider the specific heat capacity of water, the latent heat of vaporization for water, and the mass of water, given that 1m³ of water has a mass of approximately 1000 kg.

Next, considering that the Carnot engine is 40% efficient, we use this efficiency to determine the work output of the cycle. The formula for efficiency (η) is η = Work Output (W) / Heat Input (Qh), where Qh is the heat supplied to the boiler. Rearranging the formula to solve for Work Output yields W = η * Qh.

Lastly, for an isothermal reduction in steam pressure to 7 bars at 175°C, we'd reference a steam table to determine the phase of water. However, since we know that 100°C is the boiling point of water at 1 atmospheric pressure, 175°C at 7 bars indicates that the water is in the state of superheated steam.