It's exam period and we are all very busy. Can't be expecting us
to answer within mins right?
Anyway, I will give you some hints. First, 27C must be converted
to 300K, because kelvins is the SI unit of temperature.
Since the mass of the piston is such that a pressure of 400kPa
is required to move it, this means a few things (try drawing out on
a P-V diagram)
Initially, heat is supplied at constant volume. Only pressure
and temperature changes until the pressure reaches 400kPa. This is
represented by a vertical upwards line on the P-V diagram. Using
P/T as a constant, you will find that the final temperature is now
600K.
Then, because the piston will always move if the pressure of the
gas exceeds 400kPa, the pressure of the gas is thus made to stay
constant at 400kPa. This is represented by a horizontal rightwards
line on the P-V diagram. Using V/T as a constant, since volume
doubles, your final temperature T is 1200K.
So you have 3 points:
Point 1: P= 200kPa, V = V, n = n, T = 300K
Point 2: P= 400kPa, V = V, n = n, T = 600K
Point 3: P= 400kPa, V = 2V, n = n, T = 1200K
Work is only done between points 2 and 3.
n can be found by assuming air to be mostly nitrogen, so 3kg of air
can be converted to number of moles. You can thus find work done =
p (change in v) = nR (change in T)
As for heat supplied, you are only given Cv, which is heat
capacity at constant volume. Heat capacity at constant pressure is
not given. Hence, you may need to use the First Law of
Thermodynamics between points 2 and 3 after finding the work done.
Since air is mostly nitrogen and oxygen, we can assume it to be a
diatomic gas, and has 5 degrees of freedom. The internal energy
will thus be 5/2 nRT. With the change in temperature, you can
find the change in internal energy.
