How much heat is needed to increase the internal energy of a gas in a piston by 4,736J if the gas does 750J of work on the envir
1 answer:
The heat absorbed by the gas is 5486 J
Explanation:
We can solve this problem by using the 1st law of thermodynamics, which states that the change in internal energy of a gas is given by:
where:
is the change in internal energy
Q is the heat absorbed by the gas
W is the work done by the gas
In this problem, we have:
is the increase in internal energy of the gas
is the work done by the gas (positive because the gas is doing work on the surroundings, by expanding)
Solving for Q, we find the heat needed:
And the positive sign tells us that this heat is absorbed by the gas.
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a)
b) 0.43 V
c) 0.44 %
Explanation:
a)
For a battery with internal resistance, the relationship between emf of the battery and the terminal voltage (the voltage provided) is
(1)
where
V is the terminal voltage
E is the emf of the battery
I is the current
r is the internal resistance
In this problem, we have two situations:
1) when ,
Using Ohm's Law, the current is:
2) when ,
Using Ohm's Law, the current is:
Now we can rewrite eq.(1) in two forms:
And we can solve this system of equations to find r, the internal resistance. We do it by substracting eq.(2) from eq(1), we find:
b)
To find the electromotive force (emf) of the solar cell, we simply use the equation used in part a)
where
V is the terminal voltage
E is the emf of the battery
I is the current
r is the internal resistance
Using the first set of data,
is the voltage
is the current
is the internal resistance
Solving for E,
c)
In this part, we are told that the area of the cell is
While the intensity of incoming radiation (the energy received per unit area) is
This means that the power of the incoming radiation is:
This is the power in input to the resistor.
The power in output to the resistor can be found by using
where:
is the resistance of the resistor
is the current on the resistor (found in part A)
Susbtituting,
Therefore, the efficiency of the cell in converting light energy to thermal energy is: