A steam engine’s boiler completely converts
151 kg of water to steam. This process in-
volves the transfer of 4.8786 J J as heat.
If steam escaping through a safety valve
does 1.66 × 108 J of work expanding against
the outside atmosphere, what is the net
change in the internal energy of the water-
steam system?
Answer in units of J
To find the net change in the internal energy of the water-steam system, we need to consider the energy transferred as heat and the work done by the steam.
First, let's calculate the energy transferred as heat. We are given that the steam engine's boiler completely converts 151 kg of water to steam, with a heat transfer of 4.8786 J. This means the heat transferred per unit mass of water is:
Heat transferred per unit mass = Total heat transferred / Mass of water
Heat transferred per unit mass = 4.8786 J / 151 kg
Next, let's calculate the total heat transferred to the entire mass of water:
Total heat transferred = Heat transferred per unit mass * Mass of water
Total heat transferred = (4.8786 J / 151 kg) * 151 kg
Now, let's calculate the work done by the steam escaping through the safety valve. We are given that the steam does 1.66 × 108 J of work against the outside atmosphere.
Finally, the net change in the internal energy of the water-steam system is given by the equation:
Net change in internal energy = Total heat transferred - Work done
Now, substituting the values:
Net change in internal energy = [(4.8786 J / 151 kg) * 151 kg] - 1.66 × 108 J
Calculating this expression will give you the net change in the internal energy of the water-steam system.
To find the net change in the internal energy of the water-steam system, we need to consider the energy transferred as heat and the work done by the steam engine.
The net change in the internal energy (ΔU) can be calculated using the first law of thermodynamics:
ΔU = Q - W
Where:
ΔU is the net change in internal energy
Q is the heat transferred to the system
W is the work done by the system
In this case, the heat transferred to the system (Q) is given as 4.8786 J, and the work done by the system (W) is 1.66 × 10^8 J.
Substituting the given values into the equation, we have:
ΔU = 4.8786 J - 1.66 × 10^8 J
ΔU = -1.66 × 10^8 J + 4.8786 J
= -1.66 × 10^8 J - 4.8786 J
ΔU ≈ -1.66 × 10^8 J
Therefore, the net change in the internal energy of the water-steam system is approximately -1.66 × 10^8 J.