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, you are correct in using the first law of thermodynamics, which is ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat transfer, and W is the work done.

In this case, since the process is at constant pressure and there is no evaporation to the surroundings, the work done can be assumed to be zero (W = 0). Therefore, the equation simplifies to ΔU = Q.

To find the heat transfer, you can use the equation Q = m * C * ΔT, where Q is the heat transfer, m is the mass of the water, C is the specific heat capacity of water, and ΔT is the change in temperature.

First, you need to find the mass of the water that needs to be heated. The steam flow rate is given as 4 gm/min, so you need to convert it to kg/s. Since there are 60 seconds in a minute, the steam flow rate is 4 gm/min * (1 kg / 1000 gm) * (1 min / 60 s) = 0.067 kg/s.

Next, calculate the heat transfer needed to raise the temperature of the water from 278 K to 322 K. Q = m * C * ΔT = 0.17 kg * (4,186 J/kg·K) * (322 K - 278 K).

Now you have the value of Q, which represents the heat transfer needed to heat the water. Finally, you can solve for time (t) using the equation ΔU = Q = m * C * ΔT = (0.067 kg/s) * (4,186 J/kg·K) * (322 K - 278 K) * t.

Simplifying the equation, you have ΔU / (m * C * ΔT) = t. Substitute the known values, solve for t, and you will find the time it takes to heat the water to 322 K.