3.
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Answer : The temperature and the final pressure of the gas is, 586.83 K and respectively.
Explanation : Given,
Initial volume of gas =
Final volume of the gas =
Heat released = -9340 J
First we have to calculate the temperature of the gas.
According to the question, this is the case of isothermal reversible compression of gas.
As per first law of thermodynamic,
where,
= internal energy
q = heat
w = work done
As we know that, the term internal energy is the depend on the temperature and the process is isothermal that means at constant temperature.
So, at constant temperature the internal energy is equal to zero.
Thus, w = -q = 9340 J
The expression used for work done will be,
where,
w = work done = 9340 J
n = number of moles of gas = 3 mole
R = gas constant = 8.314 J/mole K
T = temperature of gas = ?
= initial volume of gas
= final volume of gas
Now put all the given values in the above formula, we get the temperature of the gas.
Now we have to calculate the final pressure of the gas by using ideal gas equation.
where,
P = final pressure of gas = ?
V = final volume of gas =
T = temperature of gas = 586.83 K
n = number of moles of gas = 3 mole
R = gas constant = 0.0821 L.atm/mole.K
Now put all the given values in the ideal gas equation, we get:
Therefore, the temperature and the final pressure of the gas is, 586.83 K and respectively.