Saturated water vapor at 100 kPa jets into a pitcher containing 0.17 Kg of water
initially at 278 K. If steam
ow rate is 4 gm/min, estimate how long it takes to heat
the water to 322 K. Assume the process is at constant pressure (at 100 kPa) and kinetic
energy of the incoming steam is negligible. Further assume that there is no evaporation
to the surrounding. If needed make other necessary assumptions and clearly identify
them.
My attempt- I know i need to look up values in a table for the internal energy of steam etc, I think i need to use dU=dQ-dW and possibly another equation.
To solve this problem, we can follow the steps outlined below:
Step 1: Find the heat transfer required to raise the temperature of the water from 278 K to 322 K.
Step 2: Calculate the change in internal energy of the water during this process.
Step 3: Determine the work done by the system.
Step 4: Use the first law of thermodynamics (dU = dQ - dW) to find the heat transfer.
Step 5: Calculate the time it takes to transfer this amount of heat based on the steam flow rate.
Step 1: Find the heat transfer required to raise the temperature of the water from 278 K to 322 K.
The heat transfer required can be calculated using the formula:
dQ = m * Cp * dT
Where:
dQ is the heat transfer (in joules)
m is the mass of water (in kg)
Cp is the specific heat capacity of water (approximately 4.184 J/g·K or 4184 J/kg·K)
dT is the change in temperature (in K)
First, convert the steam flow rate from grams to kilograms:
steam_flow_rate = 4 g/min = (4/1000) kg/min = (4/1000) / 60 kg/s
Step 2: Calculate the change in internal energy of the water during this process.
The change in internal energy can be calculated using the formula:
dU = mc * dT
Where:
dU is the change in internal energy (in joules)
mc is the specific heat capacity of water (approximately 4.186 J/g·K or 4186 J/kg·K)
dT is the change in temperature (in K)
Step 3: Determine the work done by the system.
Since the process is at constant pressure, the work done by the system is zero. This assumption allows us to simplify the equation.
Step 4: Use the first law of thermodynamics (dU = dQ - dW) to find the heat transfer.
In this case, since there is no work done, the equation becomes:
dU = dQ
Step 5: Calculate the time it takes to transfer this amount of heat based on the steam flow rate.
The equation to calculate the heat transfer is:
dQ = m_dot * dH
Where:
m_dot is the mass flow rate of steam (in kg/s)
dH is the enthalpy difference between saturated vapor at 100 kPa and the desired temperature (in joules/kg)
To find the enthalpy difference, you need to use a steam table or lookup chart to find the specific enthalpy values for saturated vapor at 100 kPa at 278 K and 322 K. The difference in enthalpy can then be calculated.
Finally, calculate the time it takes to transfer the heat:
time = dQ / (m_dot * Cp)
This will give you the estimated time it takes to heat the water to the desired temperature.